Japheth’s uncle is 10 less than three times Japheth’s age. Which of the equations represents Japheth’s uncle’s age (u) as it relates to Japheth’s age (k)?

A. u=10-3k

B. u=3k-10

C. k=3u-10

D. k=10-3u

Answer Explanation:

We are asked to determine Japheth’s uncle’s age relating to Japheth’s age.

First, express Japheth’s uncle’s age in terms of Japheth’s age as follows

Japheth’s age=k

Japheth’s uncle’s age, u = 3k-10.

Thus, the relationship between Japheth’s uncle’s age to that of Japheth is u=3k-10.

Therefore, the Correct Answer is B.

Q #1: Which of the following is the value of x in the equation below

A. x= -4 or x=2

B. x= -2 or x=3

C. x =-2 or x= 4

D. x= -2 or x= 1

Answer Explanation

we find the value of x by applying the absolute conditions to the given equation.

First, add 2 to both sides of equation

The absolute conditions are:

If , a>0, then u=a or u=-a

In this case a=10, which is greater 0.

The first condition becomes

Add 2 to both sides of the equation

Divide both sides by 4

The second condition becomes

Add 2 to both sides of the equation

Divide both sides by 4

Then, the value of x is 3 or -2.
Q #2: The American with Disabilities Act (ADA) requires that the slope of a wheelchair ramp be no greater than 1:12. Which of the following is the minimum length of a ramp needed to provide access to a door that is 1.5 feet above the sidewalk?

A. 12 feet

B. 4.5 feet

C. 3 feet

D. 18 feet

Answer Explanation

We use the given slope to find the minimum length of the ramp. In this case, slope is the ratio of height to length of the lamp. Thus,

If we let x be the minimum length of the ramp. Then,

Substituting the value of slope into the above equation results in,

Solve for value of x by cross-products

X = 18 Feet

Thus, the minimum length of the ramp needed to provide access to a door that is 1.5 high is 18 feet.
Q #3: A recipe calls for 2/9 cup of flour for every 1 2/5 cup of milk. To make a bigger batch, the chef uses 2 cups of flour. Which of the following would be the amount of milk needed for the bigger batch?

A. 12 1/5 cups

B. 12 3/5 cups

C. 8 1/25 cups

D. 10 3/25 cups

Answer Explanation

The number of cups of milk to make a bigger batch, we proceed as follows:

First convert the mixed number 1 2/5 as

Then, we let the unknown number of cups of milk to be x and we set a proportion equation with number cups of floor as numerator and cups of milk as denominator

Find the value of x by cross-products

2 as a fraction is 2/1 which is then used to find the product of the numerator as follows.

Per means division. The above equation becomes

When dividing fractions, we multiply the first fraction with the reciprocal of the second. The reciprocal of 2/9 is 9/2. Thus

The numbers of cups of milk required is 63/5, which when converted to mixed fraction becomes 12 3/5.