Question

1 cup = 8 ounces, 10 ounces = 60 teaspoons. Based on the given information above, how many teaspoons are equivalent to \[\dfrac{1}{4}\] cup?
A. 12
B. 10
C. 8
D. 6

Answer 1

Hint: To solve the question, we have to solve the two given equations and analyse the connection between quantities of cup, ounces, teaspoons to ease the procedure of solving. To solve further, find the value of \[\dfrac{1}{4}\] cup in terms of ounces and then calculate the number of teaspoons which is equivalent to the obtained ounces value.

Complete step-by-step answer:
The given relation between cup and ounces is given by 1 cup = 8 ounces
Divide the above equation by 4 on the both sides of the equation to obtain the value of \[\dfrac{1}{4}\] cup
Thus, we get
\[\dfrac{1}{4}\] cup = \[\dfrac{8}{4}\] ounces
We know that 8 is a product of 4 and 2. Thus, we get
\[\dfrac{1}{4}\] cup = \[\dfrac{4\times 2}{4}\] ounces
By cancelling the common terms on both numerator and denominator, we get
\[\dfrac{1}{4}\] cup = 2 ounces …… (1)
The given relation between teaspoons and ounces is given by 10 ounces = 60 teaspoons
The above equation can also be written as,
\[1\times 10\] ounces = \[6\times 10\] teaspoons
By cancelling the common terms on both the sides of the equation, we get
1 ounce = 6 teaspoons
By multiplying both the sides of the equation with 2, to obtain the value of 2 ounces, we get
\[1\times 2\] ounces = \[6\times 2\] teaspoons
By substituting the products of the numbers, we get
2 ounces = 12 teaspoons
By substituting the values from equation (1) in the above equation, we get
\[\dfrac{1}{4}\] cup = 12 teaspoons.
Hence, option A is the right choice.

Note: The possibility of mistake can be not able to analyse the connection between the two equations given. The alternative way of solving the question can be by using options calculation method, by which we use reverse chronology, we will calculate the options value in terms of cup to check which option is equivalent to \[\dfrac{1}{4}\] cup. Thus, we can arrive at the answer.