John’s uncle is twelve less than five times John’s age. Which of the equations represents John’s uncle’s age (u) as it relates to John’s age (k)?
u = 12-5k
k = 5u-12
k = 12-5u
u = 5k-12
Correct Answer : D
We are asked to determine John’s uncle’s age relating to John’s age.
First, express John’s uncle’s age in terms of John’s age as follows
John’s age=k
John’s uncle’s age, u = 5k-12.
Thus, the relationship between Japheth’s uncle’s age to that of Japheth is u=5k-12.
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Correct Answer is A
Explanation
To find the area of the room, we form an equation of find an equation relating the length and width of the rectangle. If we let the width of the room to be w, then
Width of the rectangle= w
Length of rectangle=(w+8)
Area of the rectangle, A= Length*width=(w+8)*w
A=w(w+8)
Thus, the area of the rectangular room is w(w+8).
Correct Answer is B
Explanation
To determine the number of sophomore students, follow these steps:
- Identify the total number of students:
1,276
- Identify the percentage of sophomores:
29%
- Calculate the number of sophomores:
(29%×1,276) = (29/100× 1,276) = 370.04
- Round to the nearest whole number:
370
Correct Answer is C
Explanation
 we use the relation 1 L=1000 mL to convert 3.9 L to mL as follows.
Thus, 3.9 L is 3900 mL.
Correct Answer is A
Explanation
we are asked to find the number of cups of flour that will be used to make 130 cookies.
First, we convert 3 ¼ into improper fraction as:
Letting x to be the number of cups of flour, we set up a proportion equation with number of cookies on numerator and number of cups of flour on the denominator becomes:
Solve the value of x by cross-products
Dividing both sides by 64, the above equation result to
Thus, the number of cups of flour needed to make 130 cookies is 845/128 cups, which is equal to 6 77/128 cups.
Correct Answer is D
Explanation
To find the required number of cups milk needed, we set a proportion equation with number of cups be numerator and cups of milk as denominator.
Let x be the number of cups of milk needed, then
The numbers of cups of milk required is 273/25, which when converted to mixed fraction becomes 10 23/25.
Correct Answer is A
Explanation
we find the value of x by applying the absolute conditions to the given equation.
First, add 2 to both sides of equation
Add 10 to both sides of the equation
Next, we apply the absolute rule:
If u=a, a>0, then u=a or u=-a
In this case a=5, which is greater 0.
The first condition becomes
Solving for x
The second condition becomes
Solving for x
Then, the value of x is -4/3 or 2.
Correct Answer is D
Explanation
the mean of a data set is the total scores divided by the number of tests.
Total test scores =80+68+74+87+96=405
Number of tests =5
Mean test score =405/5=81
The mean test score is 81.
Correct Answer is D
Explanation
To find the cheapest option, we find the expenditure on each given option.:
2 two-24 packs of Orange and 1 pack of Cream Soda=2($15)+$3=$33
3 one 24-pack of Orange=3($9)=$27
2 packs of Root Beer and 1 pack of Cream Soda=2($14)+$3=$31
5 packs of cream Soda=5($3)=$15
Spending 5 packs of cream soda is the cost-effective option.
Correct Answer is D
Explanation
We are asked to determine John’s uncle’s age relating to John’s age.
First, express John’s uncle’s age in terms of John’s age as follows
John’s age=k
John’s uncle’s age, u = 5k-12.
Thus, the relationship between Japheth’s uncle’s age to that of Japheth is u=5k-12.
Correct Answer is B
Explanation
 In this problem, we need to compare the number of dimes to quarters.
If we let p be number of pennies in the bottle. Then,
Number of quarters in the bottle = 6p
Number of nickels in the bottle = 2p
Number of dimes in the bottle =5(2p)=10p
Now relating dimes to nickels, we have
Thus, there are 5 times as many dimes as quarters in the box.
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