Question

The cost of a small picture frame is $2.99 and the cost of a large picture frame is $8.99. Last week, the number of small frames sold was three times the sale of large frames and the total sale from the frames was $233.48.

A. Write a system of equations that represent the situation.
B. Using the substitution method how many small frames and large frames were sold that week?

Answer 1

Let the number of large frames sold be X.
Therefore the number of small frames sold is 3X.

So X large frames + 3X small frames = total sales last week.

Now substitute the prices for each item and the total into above equation:

8.99X (large frames) + 3 x 2.99X (small frames) = 233.48 (total sales)
Therefore 8.99X + 8.97X = 233.48
Therefore 17.96X = 233.48
So X = 233.48 / 17.96
Therefore X = 13

So 13 large frames were sold

So if there were 3X small frames sold, there were 3 x 13 sold, which is 39

Therefore 13 large frames and 39 small frames were sold.

(I'm not sure if this is the right method for working out this problem or not, but even if it isn't, hopefully if gives you the idea ;) )