# solving word problems using a system of equations

#### shannyvp

##### New member
Mrs. Moto invested $1400 part at 5% and part at 8% her total annual income from both investments was$100. Find the amount invested at each rate.

My question:
What are the two equations?

#### chrisr

##### Full Member
It would not be fair to tell you!

Basically, it's algebra.
You can use x and y or a and b.

Here's a clue "There are 2 things you do not know"
the amount that 5% interest is earned from and the amount 8% interest is earned from.

What do we know?

They generate $100 interest, which means the sum of the 2 interests is$100.
Also we know that the 2 amounts themselves sum to \$1400.

To find 2 values you need 2 clues.

Are you familiar with solving simultaneous equations,
like 2x+5y =7 and 3x-y =4 ??

This is the same.

So what is x+y ?
Also what is x(5/100) + y(8/100) ?

Try to figure that out

#### shannyvp

##### New member
^thank you!! i think i get it now sort of

Can you help me with another one?

The Wongs drove from their house to Dayton in 2 hours. When they returned the traffic was heavier and the trip took 3 hours. If they traveled 25 km/h faster on the way to Dayton than on the way back, find their two speeds.

My question:
I can't find the two totals. Am i missing something or is there an error in the equation?
Thanks.

#### Denis

##### Senior Member
Hint:
distance = speed * time
on way back: s * 3
on way to: (s + 25) * 2