Depth · one concept from first principles · step 2 of 4

Write it as an equation with a single unknown

Two numbers have a sum of $65.5$ and a difference of $55.5$ . Find the quotient when the larger is divided by the smaller.

ExpressionsNumber system

Your answer

How to solve

Strategy Convert to Algebra — Adding the sum and the difference wipes out the smaller number entirely, leaving twice the larger one. That turns two unknowns into one in a single move.

1STEP 1

Write the two facts as equations

Call the larger number ■ and the smaller ▲. Then the sum and the difference are two sentences about them.

■ + ▲ = 65.5, ■ - ▲ = 55.5

2STEP 2

Add the two equations

The smaller number is added in one and taken away in the other, so adding them cancels it and leaves twice the larger.

65.5 + 55.5 = 121

3STEP 3

Find each number

Halve to get the larger, then take it off the sum to get the smaller.

121 ÷ 2 = 60.5, 65.5 - 60.5 = 5

4STEP 4

Divide the larger by the smaller

Now the question can be answered directly.

60.5 ÷ 5 = 12.1

Answer

12.1

Check both facts: 60.5 + 5 = 65.5 and 60.5 - 5 = 55.5, exactly as given.

Takeaway

Adding a sum and a difference cancels one of the two numbers straight away.

Write the two facts as equations
Add the two equations
Find each number
Divide the larger by the smaller

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