The ratio of pears to green apples is 1:3. If there are 150 green apples, how many pears are there?
Understand the Problem
The question is asking for the quantity of pears given the ratio of pears to green apples and the number of green apples. To solve this, we identify that for every 1 pear, there are 3 green apples. With 150 green apples, we can use the ratio to determine the number of pears by setting up a proportional relationship.
Answer
The number of pears is \( 50 \).
Answer for screen readers
The number of pears is ( 50 ).
Steps to Solve
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Identify the Ratio
The ratio of pears to green apples is given as 1:3. This means for every 1 pear, there are 3 green apples. -
Set Up the Proportion
Let the number of pears be represented as ( p ) and the number of green apples is given as 150. We can write the ratio as: $$ \frac{p}{150} = \frac{1}{3} $$ -
Cross Multiply to Solve for Pears
Cross multiplying gives: $$ 3p = 150 $$ -
Divide to Isolate ( p )
Now, divide both sides by 3 to get the value of ( p ): $$ p = \frac{150}{3} $$ -
Calculate the Number of Pears
Calculating the right side: $$ p = 50 $$
The number of pears is ( 50 ).
More Information
This solution illustrates how ratios can be used to find quantities in proportional relationships. Every time you have a known ratio, you can set up a similar proportion to find missing values.
Tips
- Confusing the ratio: Remember that a ratio of 1:3 means for every 1 part of pears, there are 3 parts of green apples. Misinterpreting this could lead to incorrect calculations.
- Not properly cross-multiplying: Ensure both sides of the equation are correctly multiplied when setting up the ratio.
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