Stuck on number problems

[tytyman]

1).The total of two numbers is 35. Four times the larger number is 4 less than five times the smaller number. Find the two numbers.

2). The sum of two numbers is 57.The larger of the two numbers is 9 less than twice the smaller, find the two numbers.

Needs some help, Thanks

 

[soroban]

Hello, tytyman!

It is a matter of translating the words to algebra ... carefully.

1)The total of two numbers is 35.
Four times the larger number is 4 less than five times the smaller number.
Find the two numbers.

Let \(\displaystyle n\) = larger number.

Then \(\displaystyle 35-n\) = smaller number.


\(\displaystyle \underbrace{\text{Four}}_4\; \underbrace{\text{times}}_{\times}\;\underbrace{\text{larger}}_{n}\;\underbrace{\text{is}}_{=}\; \underbrace{\text{four less}}_{-4}\;\underbrace{\text{than}}_{+}\;\underbrace{\text{five}}_{5}\;\underbrace{\text{times}}_{\times}\;\underbrace{\text{smaller}}_{(35-n)}\)

The equation is: .\(\displaystyle 4n \;=\;-4 + 5(35-n)\)

2) The sum of two numbers is 57.
The larger of the two numbers is 9 less than twice the smaller.
Find the two numbers.

Let \(\displaystyle n\) = larger number.

Then \(\displaystyle 57-n\) = smaller number.


\(\displaystyle \underbrace{\text{Larger}}_{n} \; \underbrace{\text{is}}_{=} \; \underbrace{\text{9 less}}_{-9} \;\underbrace{\text{than}}_{+} \;\underbrace{\text{twice}}_{2\:\times}\;\underbrace{\text{smaller}}_{(57-n)}\)

The equation is: .\(\displaystyle n \;=\;-9 + 2(57-n)\)