SOLUTION: I don't understand how to arrive at the answers to the following problems: A)One number is 2 more than 5 times another. Their product is 24. Find the numbers. B) One number i

Question 352819: I don't understand how to arrive at the answers to the following problems:
A)One number is 2 more than 5 times another. Their product is 24. Find the numbers.
B) One number is 4 times another. Their product is 4 times their sum. Find the numbers.
Thank you!
Found 2 solutions by jim_thompson5910, jrfrunner:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started

# 1

"One number is 2 more than 5 times another" means that and "Their product is 24" tells us that (x times y = 24)

Start with the second equation.

Plug in

Distribute.

Subtract 24 from both sides.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

If you want integer only answers, then the only solution is

So one number is 2 and the other is

So the two numbers are 2 and 12.
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
let x=one number
let y=the other number
--
you are given: One number is 2 more than 5 times another
x=2+5y
--
also you are told: Their product is 24
x*y=24
==
substitute x=2+5y into x*y=24 in order to reduce the problem by one variable
x*y=(2+5y)*y=24
--

--
use the quadratic formula to solve for y
where a=5, b=2 and c=-24
--
y= or
--
y=(-2-22)/10=-2.4 or y=(-2+22)/10=2
==
substitute y=-2.4 or y=2 into x=2+5y to find x
x=2+5(-2.4)=-10 and x=2+5*(2)=12
--
so the possible answers are x=-10 and y=-2.4 or x=12 and y=2

RELATED QUESTIONS
I cannot solve this problem. I know what the answer is because I used a process if... (answered by Earlsdon)
One integer is 30 more than another integer. If difference between the larger and twice... (answered by CubeyThePenguin)
write a mathematical equation for the following solutions and solve. a number is 25 more (answered by lwsshak3)
Treat the number of months X after January 1 that someone is born as uniformly... (answered by ikleyn)
I can not figure out how to do algebric word problems. Not one. If 2 is added to five (answered by ankor@dixie-net.com,Alan3354,Earlsdon)
Can you please explain the following steps for solving the equation. I understand how to... (answered by Theo)
Hello, I just need someone to check my answers for these questions. Thank You. 1. In... (answered by ikleyn)
Mark and Don are planning to sell each of their marble collections at a garage sale. If... (answered by Alan3354)
Use the information to ding a linear algebraic model that can be used to answer the... (answered by Alan3354)