A recipe requires flour and sugar in a ratio of 5:3. If the recipe uses 250 grams of flour, how much sugar is needed?
Understand the Problem
The problem describes a ratio between flour and sugar in a recipe. Given the amount of flour used (250 grams) and the ratio (5:3), you need to determine the corresponding amount of sugar required. This can be solved by setting up a proportion.
Answer
The amount of sugar needed is 150 grams.
Answer for screen readers
The amount of sugar needed is 150 grams.
Steps to Solve
- Express the ratio as a fraction
The ratio of flour to sugar is 5:3, which can be written as the fraction $\frac{5}{3}$. This means for every 5 parts of flour, there are 3 parts of sugar.
- Set up a proportion
Let $x$ be the amount of sugar needed. We can set up the following proportion:
$\frac{\text{flour}}{\text{sugar}} = \frac{5}{3} = \frac{250}{x}$
- Solve for $x$
To solve for $x$, we can cross-multiply:
$5 \cdot x = 3 \cdot 250$
$5x = 750$
Now, divide both sides by 5:
$x = \frac{750}{5}$
$x = 150$
The amount of sugar needed is 150 grams.
More Information
The ratio 5:3 can be interpreted as "For every 5 grams of flour, you need 3 grams of sugar." Since we have 250 grams of flour, which is 50 times 5 grams, we need 50 times 3 grams of sugar, which is 150 grams.
Tips
A common mistake is to set up the proportion incorrectly, for instance, inverting the ratio or assigning the values to the wrong variables. Ensure that the ratio and the corresponding quantities are in the correct order. Another mistake would be performing the cross-multiplication incorrectly, or making an arithmetic error when dividing to isolate $x$.
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