Question

Hannah and Francine have $120. Hannah and Peter have $230. Peter has six times as much as Francine. How much does Hannah have?

Answer 1

The amount that Hannah has is $98

Explanation:

Let

x-----> amount that Hannah has

y ----> amount that Francine has

z ----> amount that Peter has

we know that

`x+y=120` ----> equation A

`x+z=230` ----> equation B

`z=6y` -----> equation C

substitute equation C in equation B

`x+6y=230` ----> equation D

we have

`x+y=120` ----> equation A

`x+6y=230` ----> equation D

Solve the system of equations A and D by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (98,22)

see the attached figure

Find the value of z

`z=6y` ---->
`z=6(22)=132`

therefore

The amount that Hannah has is $98

The amount that Francine has is $22

The amount that Peter has is $132