East Highs student council plans to buy S and C for a new student center.They need to buy 25 more C than S.C cost 32 each and S cost 28 each. If the budget is 2630, how many C can they buy?

Question

Sorry for the “C” and “S”, it would not let me type anymore. C stands for chair and S stands for stool. In class, we have been learning about Algebraic Inequalities. If anyone can solve it that way, that would be of great help! And if you can explain a little, so it is easier to understand, that would also be great! Thanks!

Answer 1

Hi Kayla,

If I had my way, I'd only buy chairs, then use the leftover money in the budget to buy donuts for the staff.

Then again, that's probably why I'm never in charge of budgets. XD

Let's use your chosen variables, letting C represent the number of chairs we'll buy, and letting S represent the number of stools we'll buy.

We need to buy 25 more chairs than stools, so we can write that down as the following equation:

C = S + 25

Next, we need to write down the budget equation. Since the amount of money we spend on chairs and stools has to be less than the amount of money in our budget, we write the inequality this way:

$2630 ≥ $32C + $28S

If the inequality sign points in the other direction, we've messed up and we'll probably get disciplined for going over our budget. We can do a quick check to make sure our equation works. If I were to buy two chairs and one stool, that would cost me $32(2) + $28(1) = $92. Fortunately, we're operating in a utopian society that doesn't charge us any sales tax. Whew.

At this point, we can do a substitution with our two equations to find the solution. Let's replace C with (S + 25) and see what we end up with:

$2630 ≥ $32(S + 25) + $28S

$2630 ≥ $32S + $800 + $28S

$2630 - $800 ≥ $60S

$1830 ≥ $60S

30.5 ≥ S

Which means that we can only buy 30 stools. Buying 31 stools would put us over budget.

If we bought 30 stools, then we have to buy 55 chairs, since we need 25 more chairs than stools.

So, it looks like C = 55 and S = 30. Let's do a final check to make sure we're under our budget, since we don't want to lose our job as the budget coordinator for the new student center:

$2630 ≥ $32(55) + $28(30)

$2630 ≥ $1760 + $840

$2630 ≥ $2600

Great! We've got $30 left in our budget.

Which means, I'm buying donuts after all. :D

Hope this helped!