Question7. A antifreeze solution is mixed with a antifreeze solution to obtain 24 gallons of a antifreeze solution. Find , the number of gallons antifreeze solution used. Round to the nearest gallon, if necessary.
Studdy Solution
STEP 1
What is this asking?
We're mixing two antifreeze solutions with different concentrations to create a specific amount of a new solution, and we need to figure out how much of each original solution we used!
Watch out!
Don't mix up the amounts of each solution with their concentrations – those percentages are key!
Also, keep track of your units (gallons) throughout.
STEP 2
1. Set up the mixture equation
2. Solve for
STEP 3
Let be the number of gallons of the **30%** antifreeze solution.
Since we want a total of **24 gallons**, the amount of the **15%** solution will be gallons.
STEP 4
The **30%** solution contributes gallons of pure antifreeze.
The **15%** solution contributes gallons of pure antifreeze.
And our desired **24-gallon** mixture contains gallons of pure antifreeze.
STEP 5
The total amount of antifreeze from the two initial solutions *must* equal the amount of antifreeze in the final mixture!
So, our equation is:
STEP 6
Let's distribute and combine like terms:
STEP 7
Subtract **3.6** from both sides of the equation:
STEP 8
Divide both sides by **0.15** to find :
STEP 9
We need **16 gallons** of the **30%** antifreeze solution.
Since we need a total of **24 gallons**, we'll also need **8 gallons** of the **15%** solution.
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