Help with Math problem

Question

Suppose a certain company sells regular keyboards for $83 and wireless keyboards for $115. Last week the store sold three times as many regular keyboards as wireless. If total keyboard sales were $5,824, how many of each type were sold?

Answer 1

Let's use the variable r to represent the NUMBER of regular keyboards and the variable w represent the NUMBER of wireless keyboards. Since the store three times as many regular as wireless, we can write:

3w = r

Then since each regular keyboard costs $83 and each wireless keyboard costs $115, with a total sales of $5824, we can represent the total money spent by:

83r + 115w = $5824

To solve these two equations with two unknowns, use substitution.

From the first equation we know that r = 3w

Substitute this expression for r into the second equation and solve for w:

83r + 115w = $5824

83* 3w + 115w = 5824

249w + 115w = 5824

364w = 5824

364w/364 = 5824/364

w = 16

Therefore, 16 wireless keyboards were sold.

The number of regular keyboards will be 3 times w or 3*16 = 48 wireless keyboards.

To verify: $83 * 48 + $115 * 16 = $3984 + 1840 = $5824