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

Answer:

The amount that Hannah has is $98

Step-by-step 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