Question 1

One-eleventh of all sales at Joe's Diner are for cash. If cash sales for the week were $380, what were Joe's total sales?

Accepted Answer

The answer of One-eleventh of all sales at Joe's Diner...

Question 2

Staples sells CDs ($2.00) and boxes of computer paper ($3). If total sales were $1,560 and customers bought 5 times as many CDs as boxes of computer paper, how many CDs were sold?

Accepted Answer

Let x be the number of boxes of computer paper sold. Then, 5x is the number of CDs sold.Total sales = (2 * 5x) + (3 * x) = 156010x + 3x = 156013x = 1560x = 120Therefore, the number of CDs sold is 5x = 5 * 120 = 600.

Question 3

Jane sells 8 times as many Volvos as Melissa. If the difference in their sales is 35, how many cars did Jane sell?

Accepted Answer

Let's assume Melissa sold x Volvos. Then Jane sold 8x Volvos. The difference in their sales is 8x-x=7x, which is equal to 35. So, x=5. Therefore, Jane sold 8x5=<<8*5=40>>40 Volvos.

Question 4

Belts cost $160 per carton, and shoes cost $465 per carton. If an order comes in for a total of 88 cartons for $19,265, what is the number of cartons of belts? (Hint: Let S = cartons of shoes.)

Accepted Answer

Let S = cartons of shoes.Then, 88 - S = cartons of belts.160(88 - S) + 465S = 19,26514,080 - 160S + 465S = 19,265305S = 5,185S = 17Therefore, the number of cartons of belts is 88 - 17 = 71.

Question 5

N/8 + 6 = 58; N equals:

Accepted Answer

Subtracting 6 from both sides of the equation gives N/8 = 52. Multiplying both sides by 8 gives N = 416. Therefore, the answer is choice B.

Question 6

Lane is 10 times Mel's age. If the difference in their age is 27, how old is Mel?

Accepted Answer

Lane's age = 10 * Mel's age. If the difference is 27, then 10 * Mel's age - Mel's age = 27. Solving for Mel's age, we get Mel's age = 3.

Question 7

One-ninth of all sales at a local Subway are for cash. If cash sales for the week were $690, what were Subway's total sales?

Accepted Answer

If one-ninth of all sales are for cash, then cash sales represent 1/9 of the total sales. Let x be the total sales for the week. 
1/9 * x = $690
Solving for x: 
x = $6,210 
Therefore, Subway's total sales were $6,210.

Question 8

A local Walmart sells sweatpants ($7) and jackets ($14). If total sales were $6,160 and customers bought 8 times as many sweatpants as jackets, what would be the number of jackets sold?

Accepted Answer

Let the number of jackets sold be x.
Then the number of sweatpants sold would be 8x.
The total sales can be expressed as 14x + 7(8x) = 6,160
Simplifying the equation, we get:
x = 88
Therefore, the number of jackets sold is 88.

Question 9

What number decreased by 630 equals 1,510?

Accepted Answer

To find the original number, we add 630 to 1,510, which equals 2,140.

Question 10

Rick and Ranger sell Toyotas for Tom's Auto. Over the past year they sold 360 cars. Assuming Rick sells 5 times as many as Ranger, how many Toyotas did Ranger sell?

Accepted Answer

Let Ranger sell x cars.
Then Rick sells 5x cars.
Thus, x + 5x = 360.
Solving for x, we get x = 60.
Therefore, Ranger sold 60 cars.

Question 11

Dolls cost $140 per carton, and trucks cost $430 per carton. If an order comes in for a total of 100 cartons for $28,500, what was the number of cartons of dolls? (Hint: Let T = cartons of trucks.)

Accepted Answer

The answer of Dolls cost $140 per carton, and trucks...

Question 12

Marvin Co. sells pens ($6) and flashlights ($10). If total sales were $624 and customers bought 7 times as many pens as flashlights, what would be the number of pens sold?

Accepted Answer

Let's call the number of flashlights sold "x". 
According to the problem, customers bought 7 times as many pens as flashlights, so the number of pens sold would be 7x. 
We can set up the equation: 
6(7x) + 10x = 624 
Simplify: 
42x + 10x = 624 
52x = 624 
x = 12 
Therefore, the number of pens sold would be 7x = 7(12) = 84.

Question 13

Mike and Bill sell cars for Jangle's Auto. Over the past year they sold 640 cars. Assuming Mike sells 3 times as many as Bill, how many cars did Mike sell?

Accepted Answer

Mike sells 3 times as many cars as Bill, so if we let the number of cars Bill sold be x, then Mike sold 3x cars. Together, they sold x + 3x = 4x cars. Given that they sold 640 cars in total, we have 4x = 640. Solving for x gives x = 160 (the number of cars Bill sold), and thus Mike sold 3 * 160 = 480 cars.

Question 14

Coffee costs $12 per case, and tea costs $8 per case. If an order comes in for a total of 250 cases for $2,600, what was the specific number of cases of tea? (Hint: Let C = cases of coffee.)

Accepted Answer

Let's use the variable C for cases of coffee and T for cases of tea.
We know that the total number of cases ordered is 250:
C + T = 250
We also know that the total cost for the order is $2,600:
12C + 8T = 2600
Now we can solve this system of equations using substitution or elimination. Let's use elimination. Multiply the first equation by 8 to get:
8C + 8T = 2000
Subtract this equation from the second equation:
(12C + 8T) - (8C + 8T) = 4C = 600
C = 150
So there were 150 cases of coffee. We can substitute this back into one of the original equations to solve for T:
150 + T = 250
T = 100
Therefore, there were 100 cases of tea.

Question 15

+31 - (-16) equals:

Accepted Answer

Subtracting a negative number is the same as adding its positive counterpart, so +31 - (-16) equals +31 + 16, which equals 47.

Question 16

What number increased by 3,080 equals 5,082?

Accepted Answer

If we let x be the number we're trying to find, we can set up the equation: x + 3,080 = 5,082. Then we can solve for x:

x + 3,080 - 3,080 = 5,082 - 3,080

x = 2,002

Therefore, the answer is D) 2,002.

Question 17

C + 100 = 55; C equals:

Accepted Answer

Subtracting 100 from both sides of equation C + 100 = 55 gives C = -45. Therefore, the answer is (D) -45.

Question 18

At Shaw's Market, apples cost $10 per case and bananas cost $6 per case. If an order comes in for a total of 300 cases for $2,000, what was the specific number of cases of apples? (Hint: Let A = cases of apples.)

Accepted Answer

The answer of At Shaw's Market, apples cost $10 per...

Question 19

Q + 92 = 128; Q equals:

Accepted Answer

Subtracting 92 from both sides of the equation Q + 92 = 128 gives Q = 36. Therefore, the answer is B.

Question 20

B/8 = 90; B equals:

Accepted Answer

The answer of B/8 = 90; B equals:
...

Quiz 5: Solving for the Unknown: a How to Approach to Solving Equations