Translating to Algebra

Question

1.How many copies can be made if there is a $2 charge to use the copy machine and copies are 5 cents a piece.

2. The photo’s width is three-fifths of it’s length.

 

Answer 1

For each of these problems, you should use a variable to represent the unknown amount.  For example, in problem #1, the cost of copying is dependent on how many copies we make, so let x = number of copies.  In problem #2, the width is dependent on the photo's length, so let L = length of photos.

 

If you think about it, whenever you buy something, you multiply the number of items by the cost of each. If I get 10 copies, I'd pay $0.05*10 or $0.50.  If I get 30 copies, I'd pay $0.05*30 or $1.50.  Even though you don't know the value of x, it is still a number and works just the same way.  x copies would cost $0.05*x or 0.05x.  Adding in the one time charge for the machine gives an expressions 2 + 0.05x as the fee.

 

Similarly, if the length was 10 inches, the width would be 3/5 * 10 or 6 inches.  Even though you don't know the value of L, it is still a number.  The width would be 3/5*L.