72.9k views
5 votes
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.

User Bdhar
by
8.0k points

1 Answer

6 votes

Answer:


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

Lucy had math and reading homework tonight. Lucy can solve each math problem in 5 minutes-example-1
User Sheavens
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories