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

Answer:

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

Step-by-step 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 $5 \times x=5x$ 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 $x=\frac{105}{5} =21$

Thus the point is $(21,0)$

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

we get $y=\frac{105}{2.5} =42$

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 $y=6$