Magazine subscriptions

Question

I am selling 3 magazine subscriptions at the prices $17, $16, and $24. I sold 38 subscriptions and made $689. I sold 2 less $16 subscriptions than $17 subscriptions. how many $24 subscriptions did I sell?

Answer 1

I am selling 3 magazine subscriptions at the prices $17, $16, and $24. I sold 38 subscriptions and made $689. I sold 2 fewer $16 subscriptions than $17 subscriptions. how many $24 subscriptions did I sell?

The three subscriptions, x, y, and z, respectively are the $17, $16, and $24 amounts. From the given information, we can let

x + y + z = 38, and
17x + 16y + 24z = 689

x + (x-2) + z = 38 17x + 16(x -2) + 24z = 689
2x + z -2 = 38 17x + 16x +24z – 32 = 689
2x + z = 40 33x + 24z = 721

If z = 40 -2x, we have:
33x + 24(40 – 2x) = 721
33x – 48x + 960 = 721

-15x = -239, and

     x = 15.9333

 

y = 13.9333 since y is 2 fewer than x

15.9333 + 13.9333 + z = 38
29.86 + z = 38
z = 8.1334

This checks out:
$17 x 15.9333 + $16 x 13.9333 + $24 x 8.1334
= $689.0005 which rounds to $689

 

How is it possible to sell 15.93 subscriptions, since someone could possibly receive part of a magazine—It is not possible for x to equal 16, but it would never be partial; there, x = 15 whole magazines. Similarly, the question is for y and for z. With this thought in mind, the earnings will differ, somewhat, from $689.