# Thread: Setting up and solving equations involving percentages

1. ## Setting up and solving equations involving percentages

okay i have another word problem that i just dont understand how to set up... or where to begin

a man invested a total of \$22,000 in two investments. he made a profit of 7% on the first and 2% on the second investment. If his profit was \$920, what was the amount of each investment?

what is 7% of the first investment in terms of x?

what is 2% of the second investment in terms of x?

write an equation that says the sum of your last two answers in equal to \$920

solve this equation.

what was the amount of each investment?

2. Originally Posted by illeatyourxface
okay i have another word problem that i just dont understand how to set up... or where to begin

a man invested a total of \$22,000 in two investments. he made a profit of 7% on the first and 2% on the second investment. If his profit was \$920, what was the amount of each investment?
So what we don't know are the amounts for each investment. Since the problem wants you to indicate both in terms of x, let's first say that the amount of the first investment is x. Then,

what is 7% of the first investment in terms of x?
This would be
$0.07x$.

what is 2% of the second investment in terms of x?
If x dollars goes toward the first investment, then 22,000 - x has to go towards the second, because the total amount is 22,000. So 2% of the 2nd investment is
$0.02(22,000 - x)$.

write an equation that says the sum of your last two answers in equal to \$920
The equation would thus be
$0.07x + 0.02(22,000 - x) = 920$.

Can you take it from here and solve for x?

01

3. i got x = 9600, but how do i know what the the amount of each investment?

4. Originally Posted by illeatyourxface
i got x = 960, but how do i know what the the amount of each investment?
x = 960? That's not what I got.

EDIT: Fixed it just in time!

Whatever the answer may be, x = the amount for the 1st investment, and 22,000 - x = the amount for the 2nd investment. In other words, you take the x-value and subtract from \$22,000 to get the amount for the 2nd investment.

01

5. so the answers are 9600 and 12400??

6. Originally Posted by illeatyourxface
i got x = 9600, but how do i know what the the amount of each investment?
Look at yeogil's post again

The first investment is.....

0.07x

The second is.......

You know what x is, so use it!

7. Originally Posted by illeatyourxface
so the answers are 9600 and 12400??
Yes.

01

8. so i multiply .07 with 9600
and
.02 with 9600

as well?

9. Originally Posted by illeatyourxface
so i multiply .07 with 9600
and
.02 with 9600

as well?
No. Since 0.02 was multiplied by the expression (22,000 - x) in the original equation, you multiply 0.02 by \$12,400.

And technically, I spoke too soon earlier -- we need dollar signs next to our answers, so \$9,600 and \$12,400.

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10. im sorry, im soo confused... how do we find each investment?
do i multiply .07 too?

11. Originally Posted by illeatyourxface
im sorry, im soo confused... how do we find each investment?
do i multiply .07 too?
No, you already found the amount of each investment, \$9,600 and \$12,400. When you were asking about multiplying by 0.07 & 0.02, I thought you were checking your work.

Multiplying \$9,600 by 0.07 gives the profit made from the first investment, which is \$672.
Multiplying \$12,400 by 0.02 gives the profit made from the second investment, which is \$248.
Adding the two profits together gives us the \$920 that we needed.

01

12. ohh wait i think i get it! the \$9600 is the profit and thats why you subtract it from \$22000.

and then we get \$12,400 and the we find each investment by multiplying it by .07 and .02?

is that correct?

13. multiply 0.07 by x because in the first you had 0.07x.
for the second, multiply 0.02 by (\$22000-x)
plug the values for x since you already know it

14. thankkks so much, i appreicate it!

15. Originally Posted by arze
multiply 0.07 by x because in the first you had 0.07x.
for the second, multiply 0.02 by (\$22000-x)
plug the values for x since you already know it
wait what am i multiplying? 12,400 or 9,600??

im confused again

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