A cake recipe calls for sugar and flour in the ratio . If a baker plans to use cups of sugar, how many cups of flour should the baker use to keep the same ratio?
For ratio questions, match each given quantity to its place in the ratio, then find the scale factor between the original ratio and the new situation. Multiply all related parts of the ratio by this same factor, or set up a simple proportion like and solve for the unknown. Quickly check your answer by seeing if the new pair of numbers reduces back to the original ratio.
Hints
Connect the given sugar amount to the ratio
In the ratio , the 3 corresponds to sugar. Compare this 3 to the 12 cups of sugar the baker plans to use.
Find the scale factor
Ask yourself: by what number do you multiply 3 to get 12? The same number will be used to scale the flour amount.
Apply the scale factor to the flour
Take the 5 from the ratio (for flour) and multiply it by the same number you used to turn 3 into 12.
Desmos Guide
Use a proportion in Desmos
In the Desmos calculator, type 3/5 = 12/x and press Enter. Then either solve for using the Desmos solver (if available) or note the value of that makes both sides equal; this is the needed cups of flour.
Or use direct multiplication
Alternatively, in Desmos type 12*(5/3) and press Enter. The output shown is the number of cups of flour that keeps the ratio when using 12 cups of sugar.
Step-by-step Explanation
Understand the ratio
The recipe uses sugar and flour in the ratio . This means:
- For every 3 parts of sugar, there are 5 parts of flour. So sugar : flour .
Find the scale factor using the sugar amount
The baker will use 12 cups of sugar instead of 3 cups. Find what number multiplies 3 to give 12:
Solve:
So the amounts in the recipe are being multiplied by 4.
Apply the same scale factor to the flour
Use the same scale factor (4) on the flour amount:
- Original flour in recipe: parts
- Scaled flour:
Compute:
So the baker should use 20 cups of flour to keep the same ratio.