Lesson 4: Apply Two-Variable Relationships to Solve Problems6.AT.11

I can…

I can write an equation to represent the relationship between two variable quantities and use it to solve a real problem.

Key words

• solution — A value of the variable that makes an equation true.
• substitute — To replace a variable with a number so you can compute.
• at least — That amount or more — the smallest amount that still works.
• predict — To make a reasonable guess about a future amount using information you already have.
• justify — To explain WHY an answer or recommendation makes sense, using the mathematics.
• Equation — A math sentence with an equals sign showing two amounts are the same.
• Inverse operation — The operation that undoes another one.
• Work backward — Start from the output and undo each step to find the input.

Steps

1. The number of cars produced depends on the number of hours of operation. Every hour, the plant produces 2.5 cars.
2. Let h = hours and c = cars. The equation is c = 2.5h. Check with the table: 8 hours gives 2.5 × 8 = 20 cars per shift.
3. The order needs 1,000 cars, so substitute: 2.5h = 1,000.
4. Divide both sides by 2.5: h = 1,000 ÷ 2.5 = 400 hours.
5. Interpret it: 400 hours running 24 hours a day is about 17 days — about 2.5 weeks. That fits inside 3 weeks only if the plant runs 24 hours a day, 7 days a week.

Try it

A printer prints 1.5 pages per second. Using 1.5s = 300, how many seconds does a 300-page job take?

Check your answer

200 seconds

Divide both sides by 1.5: s = 300 ÷ 1.5 = 200 seconds. Check: 1.5 × 200 = 300 pages.

Sentence starter

I know ___ because ___.

Goal: I can justify a recommendation using the words equation, solution, and at least.