A child has a bottle full of pennies, nickels, dimes, and quarters. There are twice as many quarters as pennies, four times as many as nickels as pennies, and five times as many dimes as nickels. How many more dimes does the child have than quarters?
4 times as many
5 times as many
20 times as many
10 times as many
Correct Answer : D
In this problem, we need to compare the number of dimes to quarters.
If we let n be number of pennies in the bottle. Then,
Number of quarters in the bottle = 2n
Number of nickels in the bottle = 4n
Number of dimes in the bottle =5(4n)=20n
Now relating dimes to quarters, we have
Thus, there are 10 times as many dimes as quarters in the box.
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Correct Answer is B
Explanation
We are asked to find the number of cups of flour that will be used to make 90 cookies.
Letting x be the number of cups of flour and setting the proportion equation with number of cookies on numerator and number of cups of flour on the denominator. We have
Solve the value of x by cross-multiplying
We convert the mixed fraction into improper fraction in order to carry out multiplication
\(x =\ \frac{9}{4}\ cups\ *\ 90\ cookies\ *\ \frac{1}{36}\ cookies\)
The number of cups of flour needed to make 90 cookies is 5.625 cups, which is equal to 5 5/8 cups(Choice B).
Correct Answer is A
Explanation
To find the greatest number from the given options, we first convert the decimal numbers into fractions.
-0.7 becomes 7/10
-1.3 becomes 13/10
Then, we find the LCM for the denominators of the given fractions. The LCM of 3 and 10 is 30. Now we can multiply each fraction with the LCM.
-2/3*30=-20
-7/10*30=-70
-13/10*30=-39
-4/3*30=-40
Comparing the obtained values from above, -20 is the greatest followed by -39, -40, -70 in that order. The fraction -2/3 gave a value of -20, which was the greatest value. Thus, -2/3 is the greatest value from the given option.
Correct Answer is A
Explanation
We are being asked to find the amount of milk needed. This is a proportion problem, which compares the amount of flour to that of milk. Letting x represent the amount of milk required, we set up the proportion with flour on the numerator and amount of milk in denominator as follows:
Change the mixed fraction of 1 1/5 into improper fraction as follows
The proportion equation becomes
Cross-multiply to solve for x
As an mixed fraction, 36/5 becomes 7 1/5. Therefore, 7 1/5 cups of milk are needed to make a big batch of 2 cups.
Correct Answer is A
Explanation
To find the cost-effective option, we need to find how much the consumer will spend for the given options:
2 packs of Orange and 1 pack of Cream Soda will cost $18+$5= $23
3 Packs of Orange will cost $18+$10=$28
2 packs of Root Beer and 1 pack of Cream Soda will cost 2($12)+$5=$29
5 packs of cream Soda will cost 5($5)=$25
From the above evaluation, the consumer will spend $23 for a cost effective package of soft drinks. Thus, 2 packs of Orange and 1 pack of Cream Soda will be cheaper to purchase compared to other options.
Correct Answer is C
Explanation
We required to find the units of finding the weight of a spoon. The mass is measured in kilogram and grams. Kilograms are used to measure the mass of heavier objects while grams for small and lighter objects.
Thus, gram is the appropriate unit for measuring weight of a spoon.
Correct Answer is D
Explanation
The slope represent the ratio between the vertical height to the horizontal length. Let x be the minimum length of the ramp, we can set a proportion with height on the numerator and length on denominator. Then,
Cross-multiply to find the value of x
Thus, the minimum length of the ramp needed is 30 feet to access to a door that is 2.5 feet above the sidewalk.
Correct Answer is A
Explanation
The mean of a data set is the total scores divided by the number of tests.
Total test scores =100+78+47+84+93+78=480
Number of tests =6
Mean test score =480/6=80
The mean test score is 80.
Correct Answer is D
Explanation
We are asked to find the Kwame’s uncle’s age in terms of Kwame’s age.
First, we need to find the age of Kwame, which is k. Then, we know that Kwame’s uncle’s age is three times that of Kwame less 17. Then,
Kwame’s uncle’s age, u = 3k-17.
Thus, the relation that relates Kwame’s uncle’s age to that of Kwame is u=3k-17.
Correct Answer is C
Explanation
The question requires us to find the percentage change in weight of a person.
First, we need to find the change in weight over the 3 months
Change in weight= 180-160=20 lb
Percent change in weight is change of original weight *100. Thus
The percent change in weight is 11% to the nearest whole number.
Correct Answer is A
Explanation
We follow the order of operations to solve the given expression.
First, we start with the numerator and solve it as follows
[2(3+5*3)]
We start with multiplication in inner brackets, 5*3=15. The expression becomes
[2(3+15)]
Then, we conduct the addition of 3+15=18. Then, the expression yields
[2(18)]=2*18=36
Now, we solve for denominator, which is 12/2=6.
Thus, the expression is reduced into
The expression reduces into 6.
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