Question

Lucy had math and reading homework tonight. Lucy can solve each math problem in 5 minutes and she can read each page in 2.5 minutes. The number of math problems Lucy solved is 3 times the number of pages she read and it took her 105 minutes to complete all of her homework. Graphically solve a system of equations in order to determine the number of math problems Lucy solved,x, and the number of pages she read, y.

Answer 1

`x=18,y=6`, graph is there for reference.

Explanation:

Given,

`x` is the number of math problem Lucy solved.

`y` is the number of pages she read.

She can do each math problem in
`5` minutes, therefore she can solve
`x` number of questions into
`5 * x=5x` minutes.

She can read each page in
`2.5` minutes, therefore she can read
`y` pages in 2.5y minutes.

As per given detail,

`5x+2.5y=105` equation 1.

And,

It is given that number of math problems Lucy solved is 3 times the number of pages she read.

`x=3y` equation 2.

We need to find
`x` and
`y` intercept of each of the equation to graph them.

For
`x-intercept` put y=0

We will get
`x=(105)/(5) =21`

Thus the point is
`(21,0)`

Let us find
`y-intercept` by assuming
`x=0`

we get
`y=(105)/(2.5) =42`

Thus the point is
`(42,0)`

Join these two points.

Similarly considering the other equation
`x=3y`

Here x-intercept would be at
`y=0`

We will get
`x=0`

Thus the point is
`(0,0)`

Let us assume on more point, say
`x=30` , we get
`y=10`

Thus the point is
`(30,10)`

Join these two points.

We will get a point of intersection at
`(18,6)`

Thus
`x=18` and
`y=6`