Question

Please help with number 39

Answer 1

You want to find values of v (number of visors sold) and c (number of caps sold) that satisfy the equation

... 3v + 7c = 4480

In intercept form, this equation is

... v/(1493 1/3) + c/640 = 1 . . . . . divide by 4480

Among other things, this tells us one solution is

... (v, c) = (0, 640)

The least common multiple of 3 and 7 is 21, so decreasing the number of caps sold by some multiple of 3 and increasing the number of visors sold by that same multiple of 7 will result in another possible solution.

The largest multiple of 21 that is less than 4480 is 213. Another possible solution is (0 +213·7, 640 -213·3) = (1491, 1)

We can also pick some number in between, say using 100 as the multiple

... (0 +100·7, 640 -100·3) = (700, 340)

In summary, your three solutions could be

... (visors, caps) = (0, 640), (700, 340), (1491, 1)