# Word Problems Involving Equivalent Ratio

An equivalent ratio is a ratio that has the same relationship between numbers as another ratio, but the numbers themselves may be different.

For example, the ratio 2:4 is equivalent to the ratio 4:8 because in both cases, the relationship between the numbers is the same (1:2).

## Step-by-step guide to solving equivalent ratios word problems

To solve the equivalent ratio’s word problems, follow these steps:**Step 1:** Find the ratio given in the word problem.**Step 2:** Find the given value of one of the two values involved in the ratio**Step 3:** Divide the given value of step 2 by the corresponding value in the ratio from step 1.**Step 4: **Multiply both numbers in the original ratio by the number found in step 3 to construct the equivalent ratio.

**Word Problems Involving Equivalent Ratio – Examples 1**

If a box contains pink and green marbles in the ratio of 3:8 pink to green, how many pink marbles are there if 40 green marbles are in the box?**Solution:Step 1:** Write the ratios. \(\frac{3}{8}=\frac{x}{40}\)

**Step 2:**Use cross multiplication. \(3×40=8×x⇒120=8x\)

**Step 3:**Divide. \(x=\frac{120}{8}=15\)

**Word Problems Involving Equivalent Ratio – Examples 2**

Are these ratios equivalent? 10 books for 15 shelves, and 20 books for 25 shelves.

Solution:**Step 1: **Write the ratios. \(\frac{10}{15}, \frac{20}{25}\)**Step 2: **Use cross multiplication. \(10×25=20×15⇒250≠300\)

So these ratios are not equivalent.

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