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lilavasa [31]
3 years ago
6

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 minu

tes. 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.

Mathematics
1 answer:
drek231 [11]3 years ago
8 0

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

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