Question

1. in suri’s coin purse, she has 6 dimes and 4 quarters. martha has 5 dimes and 3 quarters. suri thinks that the ratio of dimes to quarters in both purses is the same because they each have 2 more quarters than dimes. is the same ratio of dimes to quarters maintained? justify your response. (example 1)

Explanation:

Step1: Find Suri's ratio of dimes to quarters

Suri has 6 dimes and 4 quarters. The ratio of dimes to quarters is calculated as $\frac{\text{Number of dimes}}{\text{Number of quarters}}$. So, for Suri, the ratio is $\frac{6}{4}=\frac{3}{2}$.

Step2: Find Martha's ratio of dimes to quarters

Martha has 5 dimes and 3 quarters. The ratio of dimes to quarters is $\frac{5}{3}$.

Step3: Compare the two ratios

We need to check if $\frac{3}{2}$ is equal to $\frac{5}{3}$. Cross - multiply: $3\times3 = 9$ and $2\times5=10$. Since $9
eq10$, the ratios are not equal.

Now, let's consider the case where we add 2 more quarters to each. For Suri, new number of quarters is $4 + 2=6$, dimes remain 6. New ratio: $\frac{6}{6} = 1$. For Martha, new number of quarters is $3+ 2 = 5$, dimes remain 5. New ratio: $\frac{5}{5}=1$. Wait, but the original question is about Suri's initial ratio (6 dimes, 4 quarters) and Martha's initial ratio (5 dimes, 3 quarters), and then the idea of adding 2 quarters. But the main question is about the ratio of dimes to quarters for Suri and Martha.

Suri's ratio: dimes = 6, quarters = 4, ratio = $\frac{6}{4}=\frac{3}{2}=1.5$

Martha's ratio: dimes = 5, quarters = 3, ratio = $\frac{5}{3}\approx1.67$

Since $1.5
eq1.67$, the ratio of dimes to quarters is not the same.

Answer:

The ratio of dimes to quarters is not the same. Suri's ratio of dimes to quarters is $\frac{6}{4}=\frac{3}{2}$ and Martha's ratio is $\frac{5}{3}$. Since $\frac{3}{2}
eq\frac{5}{3}$, the ratios are different. When we add 2 quarters to each (Suri: 6 dimes, 6 quarters; Martha: 5 dimes, 5 quarters), the ratio becomes 1 for both, but the original ratios (before adding 2 quarters) are different.