# Thread: [SOLVED] Inequality, word problem into equation

1. ## [SOLVED] Inequality, word problem into equation

Having trouble putting this word problem into equation form:

"George Boros can pay his housekeeper $25 dollars per week to do his laundry, or he can have the laundromat do it at a cost of 90 cents per pound for the first 10 pounds and 80 cents for each additional pound. Use an inequality to find the weight at which it is more economical to use the house keeper than the laundromat." So far I have come up with this: 25 < .9(10) + .8(x - 10) Does this inequality "look" right to anyone? Thanks. 2. Originally Posted by xv84 Having trouble putting this word problem into equation form: "George Boros can pay his housekeeper$25 dollars per week to do his laundry, or he can have the laundromat do it at a cost of 90 cents per pound for the first 10 pounds and 80 cents for each additional pound. Use an inequality to find the weight at which it is more economical to use the house keeper than the laundromat."

So far I have come up with this:

25 < .9(10) + .8(x - 10)

Does this inequality "look" right to anyone? Thanks.
That inequality doesn't work when $\displaystyle x < 10$. However, you want to find the weight at which is it more economical to use the house keeper than the laundromat, so we want to find some $\displaystyle x > 10$. Therefore, your equation works for the purpose the question.

$\displaystyle 25 < 9 + 0.8x - 8$

$\displaystyle 24 < 0.8x$

$\displaystyle 30 < x$

When the weight is greater than 30 lbs, it is optimal to use the services of the housekeeper.