# Math Help - 1 problem only

1. ## 1 problem only

Hi! Please help. I will go to class in a few minutes. I don't have an equation for it. Thanks!!!

A merchant has 3 items on sale: namely, a radio for $50, a clock for$30, and a flashlight for $1. At the end of the day, she has sold a total of 100 of the 3 items and has taken exactly$1000 on the total sales. How many radios did he sell?

2. "A merchant has 3 items on sale: namely, a radio for $50, a clock for$30, and a flashlight for $1. At the end of the day, she has sold a total of 100 of the 3 items and has taken exactly$1000 on the total sales. How many radios did he sell?"

This is not a particularly simple problem, as it is over-defined. It turns out to be a test of integer programming. However, this does not mean it should be approached initially any different than any other problem.

Step #1 - Name Stuff.

R = # of radios sold
C = # of clocks sold
F = # of flashlights sold

Thus,

R + C + F = 100
50*R + 30*C + 1*F = 1000

The most logical substitution would be F = 100 - R - C, giving

50*R + 30*C + (100 - R - C) = 1000

or

49*R + 29*C = 900

If this were a continuous problem, there would be infinitely many solutions. It's not a continuous problem. Radios and Clocks don't sell in half-units.

One thing that will help is noticing that (900 - 49*R)/29 must be an integer.

Good luck. Let's see what you get.

3. ## Guess and check

Use a table instead of a equation.
$1000-100$50-radio $30-clocks$1-flashlights
50 radios 20 clocks 30 flashlights =\$3130.
The number is too big, so you must decrease the number of radios and increase the number of clocks and/or flashlights.
Hope this helps