Question

10. A landscaper mixed two chemicals to make 75 gallons of insecticide. One chemical costs $8.60 a

gallon; the other $6.75 a gallon. The cost of the insecticide is $7.40 a gallon. How many gallons of each
chemical are used? Round answers to the nearest tenth.

Answer 1

The subject involves creating a system of equations to solve for the amount of two chemicals mixed to achieve 75 gallons of insecticide at $7.40 per gallon. By setting up equations based on total volume and cost, and solving them, the volumes of the $8.60/gallon and $6.75/gallon chemicals can be determined.

Step-by-step explanation:

A landscaper is mixing two chemicals to create 75 gallons of insecticide, with one chemical costing $8.60 per gallon and the other $6.75 per gallon. The final mixture costs $7.40 per gallon. Using a system of equations, we can find the amount of each chemical needed.

Step-by-step Solution:

1. Let x be the number of gallons of the first chemical and y be the number of gallons of the second chemical.
2. The first equation is x + y = 75 (since the total mixture is 75 gallons).
3. The second equation is based on the cost: 8.60x + 6.75y = 7.40 × 75.
4. Solve this system of equations using either substitution or elimination method.
5. Once you find x and y, round the answers to the nearest tenth to get the volume of each chemical required.

By following these steps, you will find the exact amount of each chemical needed to make up the 75 gallons of insecticide at a cost of $7.40 per gallon.