Write and solve inequalities in context

Question

Audrey has $440 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a new bicycle for $259.52. She buys 2 bicycle reflectors for $3.07 each and a pair of bike gloves for $29.12. She plans to spend some or all of the money she has left to buy new biking outfits for $72.61 each. Write and solve an inequality which can be used to determine o, the number of outfits Audrey can purchase while staying within her budget.

Answer 1

No matter what Audrey only has $440 to spend so the total of all her equipment has to be equal to or less than $440.

259.92 + 2(3.07) + 29.12 + 72.61o ≤ 440

since we are trying to figure out how many outfits she can buy at $72.61 for each one thats the number that will be attached to variable o.

Now we add up the total cost so far

72.61o + 294.78 ≤ 440

Now subtract the total cost of items we have so far to see how much remaining money she has left

72.61o ≤ 145.22

Divide by 72.61 to get the number of outfits she can buy

o = 2 outfits

Answer 2

We know that Audrey has a total of $440. She can spend all $440 or less than $440, but no more than that. When we set up our inequality, we want to have our equation ≤ 440 since that is the maximum amount of money she can spend.

She buys a new bicycle for $259.52, 2 bicycle reflectors for $3.07 each and a pair of bike gloves for $29.12. That would give us 259.52 + 2 (3.07) + 29.12 so far.

She plans to spend some or all of the money she has left to buy new biking outfits for $72.61 each. We don't know how many outfits she will end up buying, so we will use the variable o to represent the number of outfits she will buy. 72.61 times o will tell us the total cost for all of the outfits she buys.

If we put that all together, we get the following inequality:

259.52 + 2 (3.07) + 29.12 + 72.61 ≤ 440

Answer 3

259.52 + 2(3.07) + 29.12 + 72.61o ≤ 440

294.78 + 72.61o ≤ 440

72.61o ≤ 145.22

o ≤ 2

She has exactly enough money left over to purchase 2 outfits.