Question 1

If Deb s present age is expressed as $w - 7$ , then her age 7 years ago is w .

Accepted Answer

If Deb's present age is w-7, then her age w-7 years ago would be (w-7)-w = -7. This is not possible, as age cannot be negative. Therefore, the statement is false.

Question 2

Solve the equation. 0.2 x + 0.7(30 $-$ x ) = 0.2(10)
A) x = -38
B) x = 41
C) x = 36
D) x = -41
E) x = 38

Accepted Answer

The equation simplifies as follows: 0.2x + 21 - 0.7x = 2, which further simplifies to -0.5x = -19. Solving for x gives x = 38.

Question 3

Solve the equation. 0.3(30) $-$ 0.8 x + x = 0.1(40)

Accepted Answer

The answer of Solve the equation. 0.3(30) $-$ 0.8 x...

Question 4

Solve the equation. 0.2(15) + x = 0.8(20 + x )

Accepted Answer

The answer of Solve the equation. 0.2(15) + x =...

Question 5

Solve the equation. 0.2(10) $-$ x = 0.5(25 $-$ x )

Accepted Answer

The answer of Solve the equation. 0.2(10) $-$ x =...

Question 6

Set up an equation and solve the following problem. Erin starts walking from point A at 1 mile per hour. One-half hour later, Chris starts walking from point A at 6 miles per hour and follows the same route. How long (in hours) will it take Chris to catch up with Erin?
A) 0.3 hour
B) 0.1 hour
C) 0.5 hour
D) 0.05 hour
E) 0.4 hour

Accepted Answer

The answer of Set up an equation and solve the...

Question 7

Set up an equation and solve the following problem. A sum of $2,400 is invested, part of it at 10% interest and the remainder at 12%. If the interest earned by the 12% investment is $112 more than the interest earned by the 10% investment, find the amount invested at each rate.
A) $1,100 at 10%, $1,300 at 12%
B) $1,000 at 10%, $1,400 at 12%
C) $800 at 10%, $1,600 at 12%
D) $650 at 10%, $1,750 at 12%

Accepted Answer

The answer of Set up an equation and solve the...

Question 8

Solve the equation. $30 x + 31 \left( 5 \frac { 1 } { 10 } - x \right) = 90$
A) x = 106.5
B) x = 110.1
C) x = 95.8
D) x = 26.8
E) x = 68.1

Accepted Answer

The answer of Solve the equation. \(30 x + 31...

Question 9

Set up an equation and solve the following problem. How many liters of pure alcohol must be added to 20 liters of a 30% solution to obtain a 80% solution? __________ liters

Accepted Answer

The answer of Set up an equation and solve the...

Question 10

Set up an equation and solve the following problem. Suppose that the perimeter of a square equals the perimeter of a rectangle. The width of the rectangle is 12 inches less than twice the side of the square, and the length of the rectangle is 6 inches less than twice the side of the square. Find the side of the square. __________ inches

Accepted Answer

The answer of Set up an equation and solve the...

Question 11

Set up an equation and solve the following problem. How many milliliters of distilled water must be added to 10 milliliters of a 70% acid solution to reduce it to a 20% acid solution? __________ milliliters

Accepted Answer

The answer of Set up an equation and solve the...

Question 12

Set up an equation and solve the following problem. Suppose that 20 gallons of a 20% salt solution is mixed with 20 gallons of a 30% salt solution. What is the percent of salt in the resulting solution? __________%

Accepted Answer

The answer of Set up an equation and solve the...

Question 13

Set up an equation and solve the following problem. The perimeter of a triangle is 45 centimeters. The longest side is 1 centimeter longer than twice the shortest side. The other side is 4 centimeters shorter than the longest side. Find the length of longest side. __________ centimeters

Accepted Answer

The answer of Set up an equation and solve the...

Question 14

Solve the equation. 0.3 x + 0.8(25 $-$ x ) = 0.5(25)

Accepted Answer

The answer of Solve the equation. 0.3 x + 0.8(25...

Question 15

Solve the equation. $20 x + 21 \left( 3 \frac { 3 } { 4 } - x \right) = 99$ Enter your answer as a decimal if necessary.

Accepted Answer

The answer of Solve the equation. \(20 x + 21...

Question 16

Set up an equation and solve the following problem. Andy starts walking from point A at 2 miles per hour. One-half hour later, Aaron starts walking from point A at 4 miles per hour and follows the same route. How long (in hours) will it take Aaron to catch up with Andy?
A) 1 hour
B) 0.45 hour
C) 0.75 hour
D) 0.5 hour

Accepted Answer

Let's call the time it takes Aaron to catch up with Andy "t" (in hours).

In that time, Andy has already been walking for 0.5 hours (since he started earlier). So he has covered a distance of:

distance = speed x time
distance = 2 x 0.5
distance = 1 mile

Now, we need to find out how long it takes Aaron to cover the same distance that Andy has already covered plus the distance that Andy has covered while Aaron was walking. So the distance that Aaron needs to cover is:

distance = 1 mile + Andy's distance

The time it takes Aaron to cover that distance is:

time = distance / speed
time = (1 + Andy's distance) / 4

But we know that Andy's distance is equal to his speed times the time he has been walking before Aaron starts, which is 0.5 hours. So we can substitute that in the equation:

time = (1 + 2 x 0.5) / 4
time = (1 + 1) / 4
time = 0.5 hours

So it will take Aaron 0.5 hours to catch up with Andy. Answer choice D is correct.

Question 17

Set up an equation and solve the following problem. Suppose that Karen, riding her bicycle at 14 miles per hour, rode 10 miles farther than Michelle, who was riding her bicycle at 12 miles per hour. Karen rode for 30 minutes longer than Michelle. How long (in hours) did Michelle ride her bicycle?
A) 1.85 hours
B) 1.7 hours
C) 1.5 hours
D) 1.55 hours

Accepted Answer

Let the time Michelle rode be $t$ hours. Then, Karen rode for $t + 0.5$ hours. The distance Karen rode is 10 miles more than Michelle. So, for Karen, distance $= 14(t + 0.5)$ and for Michelle, distance $= 12t$. Setting up the equation: $14(t + 0.5) = 12t + 10$. Solving for $t$ gives $t = 1.5$ hours.

Question 18

Set up an equation and solve the following problem. A tank contains 40 gallons of a 60% solution of anti-freeze. How much solution needs to be drained out and replaced with pure antifreeze to obtain a 90% solution? __________ gallons

Accepted Answer

The answer of Set up an equation and solve the...

Question 19

Solve the equation. $4 x = \frac { 3 } { 2 } \left( x - \frac { 1 } { 2 } \right)$
A) x = 5
B) x = $-$ 3
C) $x = - \frac { 3 } { 10 }$
D) $x = - \frac { 1 } { 5 }$
E) x = 8

Accepted Answer

To solve the equation, we first distribute the 3/2 to get:

$$4x=\frac{3}{2}x-\frac{3}{4}$$

Next, we can simplify by moving all the terms to one side:

$$\frac{5}{2}x=-\frac{3}{4}$$

Then, we can solve for x by dividing both sides by 5/2:

$$x=-\frac{3}{4}\cdot\frac{2}{5}=-\frac{3}{10}$$

Therefore, the answer is (C).

Question 20

Set up an equation and solve the following problem. How many liters of a 30% salt solution must be mixed with 10 liters of a 80% salt solution to obtain a 50% salt solution? __________ liters

Accepted Answer

The answer of Set up an equation and solve the...

Quiz 4: Formulas and Problem Solving

If Deb s present age is expressed as w−7w - 7w−7 , then her age 7 years ago is w .

Solve the equation. 0.2 x + 0.7(30 −-− x ) = 0.2(10)

Solve the equation. 0.3(30) −-− 0.8 x + x = 0.1(40)

Solve the equation. 0.2(15) + x = 0.8(20 + x )

Solve the equation. 0.2(10) −-− x = 0.5(25 −-− x )

Set up an equation and solve the following problem. Erin starts walking from point A at 1 mile per hour. One-half hour later, Chris starts walking from point A at 6 miles per hour and follows the same route. How long (in hours) will it take Chris to catch up with Erin?

Set up an equation and solve the following problem. A sum of $2,400 is invested, part of it at 10% interest and the remainder at 12%. If the interest earned by the 12% investment is $112 more than the interest earned by the 10% investment, find the amount invested at each rate.

Solve the equation. 30x+31(5110−x) =9030 x + 31 \left( 5 \frac { 1 } { 10 } - x \right) = 9030x+31(5101​−x) =90

Set up an equation and solve the following problem. How many liters of pure alcohol must be added to 20 liters of a 30% solution to obtain a 80% solution? __________ liters

Set up an equation and solve the following problem. How many milliliters of distilled water must be added to 10 milliliters of a 70% acid solution to reduce it to a 20% acid solution? __________ milliliters

Set up an equation and solve the following problem. Suppose that 20 gallons of a 20% salt solution is mixed with 20 gallons of a 30% salt solution. What is the percent of salt in the resulting solution? __________%

Set up an equation and solve the following problem. The perimeter of a triangle is 45 centimeters. The longest side is 1 centimeter longer than twice the shortest side. The other side is 4 centimeters shorter than the longest side. Find the length of longest side. __________ centimeters

Solve the equation. 0.3 x + 0.8(25 −-− x ) = 0.5(25)

Solve the equation. 20x+21(334−x)=9920 x + 21 \left( 3 \frac { 3 } { 4 } - x \right) = 9920x+21(343​−x)=99 Enter your answer as a decimal if necessary.

Set up an equation and solve the following problem. Andy starts walking from point A at 2 miles per hour. One-half hour later, Aaron starts walking from point A at 4 miles per hour and follows the same route. How long (in hours) will it take Aaron to catch up with Andy?

Set up an equation and solve the following problem. Suppose that Karen, riding her bicycle at 14 miles per hour, rode 10 miles farther than Michelle, who was riding her bicycle at 12 miles per hour. Karen rode for 30 minutes longer than Michelle. How long (in hours) did Michelle ride her bicycle?

Set up an equation and solve the following problem. A tank contains 40 gallons of a 60% solution of anti-freeze. How much solution needs to be drained out and replaced with pure antifreeze to obtain a 90% solution? __________ gallons

Solve the equation. 4x=32(x−12) 4 x = \frac { 3 } { 2 } \left( x - \frac { 1 } { 2 } \right) 4x=23​(x−21​)

Set up an equation and solve the following problem. How many liters of a 30% salt solution must be mixed with 10 liters of a 80% salt solution to obtain a 50% salt solution? __________ liters

If Deb s present age is expressed as $w - 7$ , then her age 7 years ago is w .

Solve the equation. 0.2 x + 0.7(30 $-$ x ) = 0.2(10)

Solve the equation. 0.3(30) $-$ 0.8 x + x = 0.1(40)

Solve the equation. 0.2(10) $-$ x = 0.5(25 $-$ x )

Solve the equation. $30 x + 31 \left( 5 \frac { 1 } { 10 } - x \right) = 90$

Solve the equation. 0.3 x + 0.8(25 $-$ x ) = 0.5(25)

Solve the equation. $20 x + 21 \left( 3 \frac { 3 } { 4 } - x \right) = 99$ Enter your answer as a decimal if necessary.

Solve the equation. $4 x = \frac { 3 } { 2 } \left( x - \frac { 1 } { 2 } \right)$