find two numbers such that their difference is 11 and....

[patti72458]

The difference between two numbers is 11. Twice the smaller plus three times larger is 123. What are the numbers?

 

[TchrWill]

Re: find numbers

The difference between two numbers is 11. Twice the smaller plus three times larger is 123. What are the numbers?

A - B = 11 and 2B + 3A = 123

Can you take it from her through substitution.

 

[jonboy]

Re: find numbers

Hello patti!

the difference between two numbers is 11. Twice the smaller plus three times
larger is 123. What are the numbers?

Ok we are going to have a system of equations:

The difference between two numbers is 11= \(\displaystyle \L\bold b-a=11\)

We will call \(\displaystyle \L\bold b\) the bigger number and \(\displaystyle \L\bold a\) the smaller number.

Twice the smaller plus three times larger is 123= \(\displaystyle \L\bold 2a-3b=123\)

Like TchrWill said we need to use subsitution.

\(\displaystyle \L\bold b-a=11\to b=11+a\)

Subsitution: \(\displaystyle \L\bold 2a-3(11+a)=123\)

\(\displaystyle \L\bold 2a-33-3a=123\)

Subtraction Property & Simplification: \(\displaystyle \L\bold -1a=156\)

Division Property \(\displaystyle \L\bold a=-156\)

Fill that back in one of our original equations: \(\displaystyle \L\bold b+156=11\)

\(\displaystyle \L\bold b=-145\)

 

[skeeter]

Twice the smaller plus three times larger is 123.

jonboy, do the two values you came up with, b = -90 and a = -101, make this part of the problem true? :roll:

 

[jonboy]

Twice the smaller plus three times larger is 123.

jonboy, do the two values you came up with, b = -90 and a = -101, make this part of the problem true? :roll:

It does now.