Question

Write and solve an equation for the following situation. be sure to define your variables

Each morning, Jerry delivers the Times to one neighborhood and then the Star to a different neighborhood. While delivering the Times, Jerry delivers 2 papers per minute. However, since the Star is so heavy, he can only deliver 1 Star paper per minute. If he delivers a total of 91 papers and takes exactly an hour to deliver all papers, how many of each type of paper does he deliver? ​

Answer 1

Let X be the number of Times

papers that Jerry delivers while on his first route. Let Y be the number of Star papers that Jerry delivers while on his second route.

The total number of papers he delivers is 91. So we can write: X+Y=91

He can deliver 2 Times papers per minute and it takes him X\/ 2 minutes to deliver all the Times papers. He can deliver 1 Star paper per minute and it takes him Y/1 minutes to deliver all the Star papers. We know he took exactly one hour, or 60 minutes, to deliver all of the papers, so we can write: X\/2+Y\/1=60

We can simplify the second equation by multiplying both sides by 2 to get rid of the fraction: X + 2Y = 120

Now we have two equations with

two unknowns: x + y = 91

X + 2Y = 120

We can solve for one of the variables in one of the equations and substitute into the other equation to solve for the other variable. Substituting x = 91 - y into the second equation, we get: (91 - Y) + 2Y = 120 91 + Y = 120 Y = 29

Substituting Y = 29 into the first equation, we get:

X + 2Y = 120

We can solve for one of the variables in one of the equations and substitute into the other equation to solve for the other variable. Substituting x = 91 - y into the second equation, we get: (91 - Y) + 2Y = 120 91 + Y = 120

Y = 29

Substituting Y = 29 into the first equation, we get: X + 29 = 91

X = 62

Therefore, Jerry delivers 62 Times papers and 29 Star papers.