The ratio of blueberries to strawberries is 1:7. If there are 210 strawberries, how many blueberries are there?

Understand the Problem

The question is asking us to find the number of blueberries given the ratio of blueberries to strawberries (1:7) and the total number of strawberries (210). To solve it, we will set up a proportion based on the ratio and solve for the number of blueberries.

Answer

30

Steps to Solve

Understand the ratio The ratio of blueberries to strawberries is given as 1:7. This means that for every 1 blueberry, there are 7 strawberries.
Set up the variables Let ( b ) represent the number of blueberries. According to the ratio, the number of strawberries can be represented as ( 7b ).
Use the total number of strawberries We know that the total number of strawberries is 210. We can set up the equation: $$ 7b = 210 $$
Solve for blueberries To find ( b ), we divide both sides of the equation by 7: $$ b = \frac{210}{7} $$
Calculate the result Now perform the division: $$ b = 30 $$

The number of blueberries is $30$.

More Information

This solution shows how to use proportions based on a given ratio to find an unknown quantity. Understanding ratios is essential in similar problems, especially in real-life situations like cooking or mixing ingredients.

Tips

Confusing the ratio by interpreting it the wrong way (e.g., thinking the number of strawberries is 1 instead of 7 for each blueberry).
Forgetting to set the equation correctly based on the total given.

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