Question 1

Solve the problem.

-Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 14 shares of the more valuable stock and 31 shares of the other stock. His total assets in
Stocks is $1829. How much is the more expensive stock worth per share?

Accepted Answer

Let's say the cheaper stock is worth $x per share. Then, the more expensive stock must be worth $2x per share.

Matthew has 31 shares of the cheaper stock, so the total value of those shares is 31x.

Matthew has 14 shares of the more expensive stock, so the total value of those shares is 14 * 2x = 28x.

The total value of all of his stocks is $1829. So:

31x + 28x = 1829
59x = 1829
x ≈ 31

So, the cheaper stock is worth about $31 per share. Therefore, the more expensive stock is worth about $62 per share, which is choice C.

Question 2

Solve the problem.

-What number is $18 \frac { 1 } { 5 } \%$ of 47 ? Express your answer as a mixed number.

Accepted Answer

The answer of Solve the problem.

-What number is \(18 \frac...

Question 3

Solve the problem.

-Roberto invested some money at 6%, and then invested $2000 more than twice this amount at 10%. His total annual income from the two investments was $3840. How much was invested at 10%?

Accepted Answer

Let x be the amount invested at 6%.
Then the amount invested at 10% is 2x+2000.

The income from the 6% investment is:

0.06x

The income from the 10% investment is:

0.1(2x+2000)

The problem tells us that the total income is $3840, so we have the equation:

0.06x + 0.1(2x+2000) = 3840

Simplifying:

0.06x + 0.2x + 200 = 384

0.26x = 3680

x = 14230.77 (rounded to two decimal places)

So, the amount invested at 10% is:

2x+2000 = 2(14230.77)+2000 = 30461.54

Therefore, the answer is C: $30,000.

Question 4

Solve the problem.

-0.8% of 7000 is what number?

Accepted Answer

0.8% of 7000 is calculated as (0.8/100) * 7000 = 56.

Question 5

Solve the problem.

-A writer received $39,000 as royalty for her book. She invested part of the money in bonds paying 6% interest annually. The rest she invested in a life insurance policy paying 12% interest annually.
If the total interest from the investments after 1 year is $4080, how much did she invest in bonds?

Accepted Answer

Let x be the amount invested in bonds, then 39000-x is the amount invested in the life insurance policy.
The interest earned on the bonds is 0.06x and the interest earned on the life insurance policy is 0.12(39000-x).
The total interest earned after 1 year is given as $4080.
So, we have the equation: 0.06x + 0.12(39000-x) = 4080
Simplifying and solving for x, we get:
0.06x + 4680 - 0.12x = 4080
-0.06x = -600
x = 10000
Therefore, the writer invested $10,000 in bonds.

Question 6

Solve the problem.

-Mardi received an inheritance of $60,000. She invested part at 12% and deposited the remainder in tax-free bonds at 10%. Her total annual income from the investments was $6600. Find the amount
Invested at 12%.

Accepted Answer

Let x be the amount invested at 12%, then the remainder (60000 - x) is invested at 10%. The total income is the sum of the interests from both investments: 0.12x + 0.10(60000 - x) = 6600. Solving this equation for x gives x = $30,000.

Question 7

Solve the problem.

-10.32 is 24% of what number?

Accepted Answer

To find the number that 10.32 is 24% of, you divide 10.32 by 0.24, which gives you 43.

Question 8

Solve the problem.

-$17.6$ is $14 \frac { 2 } { 7 } \%$ of what number?

Accepted Answer

To find the number that $17.6$ is $14 \frac{2}{7}\%$ of, convert the percentage to a decimal and solve for the number. $14 \frac{2}{7}\% = \frac{100}{7}\% = 0.142857$. So, $17.6 = 0.142857 \times \text{number}$. Solving for the number gives $\text{number} = \frac{17.6}{0.142857} = 123.2$.

Question 9

Solve the problem.

-Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 14 shares of the more valuable stock and 27 shares of the other stock. His total assets in
Stocks is $2640. How much is the less expensive stock worth per share?

Accepted Answer

Let x be the worth per share of the less expensive stock. Then the more valuable stock is worth 2x per share. The total value of the stocks is given by 14(2x) + 27(x) = 2640. Solving for x gives x = 48.

Question 10

Solve the problem.

-Kevin invested money in a savings account at a rate of 5% simple interest. After one year, he has $4935.00 in the account. How much did Kevin originally invest?

Accepted Answer

We can use the formula for simple interest:

I = P * r * t

where I is the interest earned, P is the principal (original investment), r is the interest rate as a decimal, and t is the time in years.

In this problem, we know that Kevin earned $4935.00 in interest after one year and that the interest rate was 5%. Plugging in these values into the formula, we get:

4935 = P * 0.05 * 1

Solving for P, we get:

P = 4935 / 0.05

P = 98,700

Therefore, Kevin originally invested $98,700. However, this is not one of the answer choices. We need to look for the answer choice that is closest to this value.

Of the answer choices given, C is the closest to $98,700. Therefore, the answer is C: $4700.00.

Question 11

Solve the problem.

-78.0 is what percent of 8? Round to the nearest tenth of a percent.

Accepted Answer

To find out what percentage 78.0 is out of 8, we can use the formula: (78.0 / 8) x 100 = 975%. Rounded to the nearest tenth of a percent, the answer is 975.0%. Therefore, the correct choice is B.

Question 12

Solve the problem.

-21.44 is what percent of 32?

Accepted Answer

To find what percent 21.44 is of 32, divide 21.44 by 32 and multiply by 100. $ \frac{21.44}{32} \times 100 = 67\%$.

Question 13

Solve the problem.

-70% of 300 is what number?

Accepted Answer

To find out what number is 70% of 300, we can first calculate what 100% of 300 is by multiplying 300 by 1, which equals 300. Then, we can find 70% of 300 by multiplying 300 by 0.7, which equals 210. Therefore, the answer is choice B, 210.

Question 14

Solve the problem.

-961 is what percent of 798? Round to the nearest tenth of a percent.

Accepted Answer

To find what percent 961 is of 798, divide 961 by 798 and then multiply by 100. $ \frac{961}{798} \times 100 \approx 120.4\% $.

Question 15

Solve the problem.

-What number is 84% of 297?

Accepted Answer

To find 84% of 297, multiply 297 by 0.84: $297 \times 0.84 = 249.48$.

Question 16

Solve the problem.

-Tim invested $87,000 in two plans. Plan 1 is at an APR of 6%, and plan 2 is at an APR of 12%. If he invested $5000 less in plan 2 than in plan 1, how much can he expect to earn in one year?

Accepted Answer

Let's call the amount Tim invested in Plan 1 "x". Then we know that the amount he invested in Plan 2 is "x-5000".

To find out how much he can expect to earn in one year, we need to calculate the interest earned on each plan and then add them together.

Interest earned on Plan 1 = x * 0.06 
Interest earned on Plan 2 = (x-5000) * 0.12

Total interest earned = (x*0.06) + ((x-5000)*0.12)

We also know that Tim invested a total of $87,000, so:

x + (x-5000) = 87000 
2x - 5000 = 87000 
2x = 92000 
x = 46000

Now we can substitute x back into our equation for total interest earned:

Total interest earned = (46000*0.06) + ((46000-5000)*0.12) 
Total interest earned = $2760 + $4920 
Total interest earned = $7680

So Tim can expect to earn $7680 in one year. Therefore, the answer is C.

Question 17

Solve the problem.

-Matthew has two different stocks. One of the stocks is worth $9 more per share than the other. He has 16 shares of the more valuable stock and 32 shares of the other stock. His total assets in stocks
Is $2208. How much is the more expensive stock worth per share?

Accepted Answer

Let x be the value of the cheaper stock, then the more expensive stock is worth x + 9. 
Matthew's total assets in stocks is the sum of the products of the number of shares and the value per share of each stock: 
16(x + 9) + 32x = 2208 
Simplifying and solving for x: 
16x + 144 + 32x = 2208 
48x = 2064 
x = 43 
Therefore, the more expensive stock is worth x + 9 = 43 + 9 = $52 per share.

Question 18

Solve the problem.

-Walt made an extra $7000 last year from a part-time job. He invested part of the money at 9% and the rest at 10%. He made a total of $660 in interest. How much was invested at 10%?

Accepted Answer

Let x be the amount invested at 9%, then (7000 - x) is the amount invested at 10%. The equation for the total interest is: 0.09x + 0.10(7000 - x) = 660. Solving this equation gives x = 4000, so the amount invested at 10% is 7000 - 4000 = 3000.

Question 19

Solve the problem.

-Annika invested in a plan that has an APR of 8%. She invested in a 11% APR account $2500 more than she invested in the 8% account. If the total interest from the investments after 1 year is $3695,
Then what is the total amount that she invested?

Accepted Answer

Let x be the amount invested in the 8% account. Then, the amount invested in the 11% account is x + 2500. The interest earned from the 8% account is 0.08x, and the interest earned from the 11% account is 0.11(x + 2500). The total interest earned is 0.08x + 0.11(x + 2500) = 3695. Solving for x, we get x = 20000. Therefore, the total amount invested is x + (x + 2500) = 45000.

Question 20

Solve the problem.

-Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on
The two investments amounts to 11%?

Accepted Answer

The answer of Solve the problem.

-Helen Weller invested $14,000 in...

Quiz 2: Linear Equations

Solve the problem. -Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 14 shares of the more valuable stock and 31 shares of the other stock. His total assets in Stocks is $1829. How much is the more expensive stock worth per share?

Solve the problem. -What number is $18 \frac { 1 } { 5 } \%$ of 47 ? Express your answer as a mixed number.

Solve the problem. -Roberto invested some money at 6%, and then invested $2000 more than twice this amount at 10%. His total annual income from the two investments was $3840. How much was invested at 10%?

Solve the problem. -0.8% of 7000 is what number?

Solve the problem. -Mardi received an inheritance of $60,000. She invested part at 12% and deposited the remainder in tax-free bonds at 10%. Her total annual income from the investments was $6600. Find the amount Invested at 12%.

Solve the problem. -10.32 is 24% of what number?

Solve the problem. - $17.6$ is $14 \frac { 2 } { 7 } \%$ of what number?

Solve the problem. -Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 14 shares of the more valuable stock and 27 shares of the other stock. His total assets in Stocks is $2640. How much is the less expensive stock worth per share?

Solve the problem. -Kevin invested money in a savings account at a rate of 5% simple interest. After one year, he has $4935.00 in the account. How much did Kevin originally invest?

Solve the problem. -78.0 is what percent of 8? Round to the nearest tenth of a percent.

Solve the problem. -21.44 is what percent of 32?

Solve the problem. -70% of 300 is what number?

Solve the problem. -961 is what percent of 798? Round to the nearest tenth of a percent.

Solve the problem. -What number is 84% of 297?

Solve the problem. -Tim invested $87,000 in two plans. Plan 1 is at an APR of 6%, and plan 2 is at an APR of 12%. If he invested $5000 less in plan 2 than in plan 1, how much can he expect to earn in one year?

Solve the problem. -Matthew has two different stocks. One of the stocks is worth $9 more per share than the other. He has 16 shares of the more valuable stock and 32 shares of the other stock. His total assets in stocks Is $2208. How much is the more expensive stock worth per share?

Solve the problem. -Walt made an extra $7000 last year from a part-time job. He invested part of the money at 9% and the rest at 10%. He made a total of $660 in interest. How much was invested at 10%?

Solve the problem. -Annika invested in a plan that has an APR of 8%. She invested in a 11% APR account $2500 more than she invested in the 8% account. If the total interest from the investments after 1 year is $3695, Then what is the total amount that she invested?

Solve the problem. -Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on The two investments amounts to 11%?

Quiz 2: Linear Equations

Solve the problem. -Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 14 shares of the more valuable stock and 31 shares of the other stock. His total assets in Stocks is $1829. How much is the more expensive stock worth per share?

Solve the problem. -What number is 1815%18 \frac { 1 } { 5 } \%1851​% of 47 ? Express your answer as a mixed number.

Solve the problem. -Roberto invested some money at 6%, and then invested $2000 more than twice this amount at 10%. His total annual income from the two investments was $3840. How much was invested at 10%?

Solve the problem. -0.8% of 7000 is what number?

Solve the problem. -Mardi received an inheritance of $60,000. She invested part at 12% and deposited the remainder in tax-free bonds at 10%. Her total annual income from the investments was $6600. Find the amount Invested at 12%.

Solve the problem. -10.32 is 24% of what number?

Solve the problem. - 17.617.617.6 is 1427%14 \frac { 2 } { 7 } \%1472​% of what number?

Solve the problem. -Matthew has two different stocks. One of the stocks is worth twice as much per share as the other. He has 14 shares of the more valuable stock and 27 shares of the other stock. His total assets in Stocks is $2640. How much is the less expensive stock worth per share?

Solve the problem. -Kevin invested money in a savings account at a rate of 5% simple interest. After one year, he has $4935.00 in the account. How much did Kevin originally invest?

Solve the problem. -78.0 is what percent of 8? Round to the nearest tenth of a percent.

Solve the problem. -21.44 is what percent of 32?

Solve the problem. -70% of 300 is what number?

Solve the problem. -961 is what percent of 798? Round to the nearest tenth of a percent.

Solve the problem. -What number is 84% of 297?

Solve the problem. -Tim invested $87,000 in two plans. Plan 1 is at an APR of 6%, and plan 2 is at an APR of 12%. If he invested $5000 less in plan 2 than in plan 1, how much can he expect to earn in one year?

Solve the problem. -Matthew has two different stocks. One of the stocks is worth $9 more per share than the other. He has 16 shares of the more valuable stock and 32 shares of the other stock. His total assets in stocks Is $2208. How much is the more expensive stock worth per share?

Solve the problem. -Walt made an extra $7000 last year from a part-time job. He invested part of the money at 9% and the rest at 10%. He made a total of $660 in interest. How much was invested at 10%?

Solve the problem. -Annika invested in a plan that has an APR of 8%. She invested in a 11% APR account $2500 more than she invested in the 8% account. If the total interest from the investments after 1 year is $3695, Then what is the total amount that she invested?

Solve the problem. -Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on The two investments amounts to 11%?

Solve the problem. -What number is $18 \frac { 1 } { 5 } \%$ of 47 ? Express your answer as a mixed number.

Solve the problem. - $17.6$ is $14 \frac { 2 } { 7 } \%$ of what number?