Algebra help

Question

The sum of three number is 12. the sum of twice the first number , 5 times the second number , & 6 times the third number is 64. The difference between 4 times the first number and the second number is 0. Find the three numbers

Answer 1

there are generally two challenges in a word problem: translating it to equations, and solving the equations.

I’ll guess your challenge is translation.

 

First, identify the quantities of interest.

let f be the “first number”

let s be the “second number”

let t be the ”third number”

 

Next, Translate the sentences into equations.

 

Notice each sentence ends with “is” some number. Translate each ”is” into an equals sign.

First, Translate “the sum of three numbers” into “f+s+t” , making the first equation

f+s+t=12

Second equation: Translate “the sum of Twice the first number, 5 times the second number, and 6 times the third number” into ”2f+5s+6t”, yielding

2f+5s+6t=64

Third equation: Translate “the difference between four times the first and the second” into “4f-s”, yielding

4f-s=0

 

At this point, you have three equations in three unknowns, which you can probably solve. As a hint, I’ll point out that the third equation is equivalent to “s=4f”. You can plug that value in for s in the other two equations, and then I’m sure you know how to solve two equations.