# Simultaneous equation help

• Feb 20th 2009, 08:16 AM
preid
Simultaneous equation help
Here is the question:

I ate 4 plates of green bananas and bought 10 pounds of dried beans. My weight (including the beans) had increased by 10%. I quickly went on a diet and returned to my original weight. Next time I ate twice as many plates of bananas and bought 10 pounds of maize flour. I weighed myself (including flour) and found my weight had increased by 11%. What was my original weight?

This is what I have so far:

1.10x = x + a + 10
1.11x = x + 2a + 10

I'm unsure on how to proceed. I've tried lots of different ways but none of them make any sense.

Thanks for any help.
• Feb 20th 2009, 10:07 AM
stapel
Quote:

Originally Posted by preid
I ate 4 plates of green bananas and bought 10 pounds of dried beans. My weight (including the beans) had increased by 10%. I quickly went on a diet and returned to my original weight. Next time I ate twice as many plates of bananas and bought 10 pounds of maize flour. I weighed myself (including flour) and found my weight had increased by 11%. What was my original weight?

This is what I have so far:

1.10x = x + a + 10
1.11x = x + 2a + 10

For what do "x" and "a" stand? I think you have defined "x" to be "my original weight" and "a" to be "the weight of the food I ate" or "the weight added by four plates of fruit". If so, your equations look fine.

Quote:

Originally Posted by preid
I'm unsure on how to proceed.

You have created a "system" of equations. There are many methods for solving a system of linear equations, but I would suggest simplifying and then using "addition".

First, study a few online lessons to learn the basics. Then:

. . . . .1.10x = 1x + 1a + 10
. . . . .1.11x = 1x + 2a + 10

. . . . .0.10x = 1a + 10
. . . . .0.11x = 2a +10

. . . . .10x = 100a + 1000
. . . . .11x = 200a + 1000

Multiplying the first equation by -2, you get:

. . . . .-20x = -200a - 2000
. . . . ..11x = .200a + 1000

Add down, and solve for the value of x. Then back-substitute to solve for the value of a.

Have fun! :D