Question

*The sum of two numbers is 400. If the first number is decreased by 20% and the second number is decreased by 15%, then the sum would be 68 less. Find the numbers after the decrease.

Answer 1

128 and 204. your welcome.

Explanation:

Let x = the first number

Let y = the second number

So we can set up two equations:

x+y = 400

.8x + .85y = 400-68

Use substitution:

y = 400 - x

.8x + (.85)*(400-x) = 332

.8x + 340 -.85x = 332

8 = .05x

x = 160

So that makes y = 240

We want the decreased values so:

160*.8 = 128

240*.85 = 204

So the answers are 128 and 204

Answer 2

The two numbers are .8*160=128 and .85*240=204

Explanation:

First sentence: x+y=400

Second sentence .8x+.85y=400-68

Solve y in the first sentence: y=400-x

Plug first into second: .8x+.85(400-x)=332

Distribute: .8x+.85(400)-.85x=332

Combine like terms: -.05x+.85(400)=332

Simplify(multiply): -.05x+ 340=332

Subtract 340 on both sides: -.05x =332-340

Simplify(subtract): -.05x =-8

Divide both sides by -.05: x =-8/-.05

Simplify (division): x = 160

So y=400-x=400-160=240