word problem

Question

A Web music store offers two versions of a popular song.

The size of the standard version is 2.9 megabytes (MB).

The size of the high-quality version is 4.4 MB.

Yesterday, there were 790
downloads of the song, for a total download size of
2681
MB. How many downloads of the high-quality version were there?

Answer 1

This question is going to give us a system of two equations. This means there will be two variables to solve for(the # of times each size was downloaded). With two equations and two variables we will be able to solve the system.

 

We will name the two variables S and H, for the number of downloads for standard and high-quality, respectively. So how do we get these equations that I mentioned earlier? We take it from the word problem.

 

The first equation comes from the fact that 790 copies were downloaded. We can represent it like this:

 

S + H = 790

 

The second equation come from the total download size of 2681. This is represented with the following equation:

 

2.9 * S + 4.4 * H = 2681

 

In this equation we are multiplying the number of Standard downloads by the size of each download to find the total contribution of S downloads to the total of 2681. The case is the same for H.

 

Now with these two equations we can substitute and solve. As this is a word problem the hardest part was setting it up, so I'll leave this bit of legwork to you. Leave a comment if you still need help.

 

Good luck!

Answer 2

a) Define the variables: X is the size of standard, Y is size of the high-quality, a is the quantity of standard downloads, b is the quantity of high-quality downloads

 

b) Set up the relationship between variables.

X=2.9, Y=4.4

Y - X = 4.4 - 2.9 = size difference = 1.5

gives

relation 1) X + 1.5 = Y

relation 2) X*a + Y*b = 2681

relation 3) a + b = 790

 

c) Solve the equations.

Substitute 1 into 2 gives

X*a + (X + 1.5)*b = 2681

X*a + X*b + 1.5*b = 2681

X*(a + b) + 1.5*b = 2681

Substitute 3 into above gives

X*(790) + 1.5*b =2681

Substitute X=2.9 into above gives

2.9*790 + 1.5*b = 2681

2291 + 1.5*b = 2681

1.5*b = 390

b = 260, which is the answer