Question

Frenklin and Ruth had 56 cents and $\$1$ respectively. They went to market and both of them bought equal number of cupcakes. Cost of Frenklin's cupcakes was same but different from Ruth's cupcakes and vice-versa.
Find the minimum cost of cupcakes bought by Frenkin and Ruth.

• A. Cost of Frenklin's cupcakes was $14\text{cents}$
• B. Cost of Ruth's cupcakes was $25\text{cents}$
• C. Cost of Frenklin's cupcakes was $4\text{cents}$
• D. Cost of Frenklin's cupcakes was $10\text{cents}$

Answer 1

Answer: (A), (B)

Cost of Ruth's cupcakes was $25\text{cents}$

We know that $\$1=100¢$

To find minimum cost of cupcakes, possible number of cupcakes bought by both of them must be maximum.

Given that both of them bought equal number of cupcakes.

They bought equal number of cupcakes and maximum possible number of cupcakes using 56 cents and 100 cents individually.

Hence, we need to find greatest common divisor of 56 and 100 to find required number of cupcakes.

Factor trees for $56$ and $100$ are


$\therefore 56=2\times 2\times 2\times 7$
And, $100=2\times 2\times 5\times 5$
$\therefore$ GCD $=2\times 2=4$

Hence, each of them bought 4 cupcakes.

Cost of cupcakes bought by Frenklin $=\frac{56\text{cents}}{4}=14\text{cents}$

Cost of cupcakes bought by Ruth $=\frac{100\text{cents}}{4}=25\text{cents}$