Inequality Word Problems Examples

Christy is playing an online game mining precious jewels, and she comes across a mother lode of emeralds. The most she's ever mined is 4 blocks of emeralds. Write an inequality expressing how many blocks she needs to mine to beat her record.

The number of blocks Christy mines needs to be greater than 4. If x represents the number of blocks she mines, then an inequality representing this would be:

x > 4

Farmer Ted is putting up a chain link fence around a rectangular garden plot. He has 75 feet of fence and wants the garden to be 15 feet wide. Write an inequality expressing the possible length of the garden plot.

The perimeter of a rectangle is 2l + 2w = perimeter, where l is the length and w is the width. We know that the total perimeter needs to be less than or equal to 75, because that's all the fencing Farmer Ted has. So the inequality looks like this.

2l + 2w ≤ 75

We also know the width is 15, so we can swap out w for 15.

2l + 2(15) ≤ 75

Now solve this bad boy for l.

2l + 2(15) ≤ 75
2l + 30 ≤ 75
2l + 30 – 30 ≤ 75 – 30
2l ≤ 45

Divide by 2 to get l by itself.

l ≤ 22.5

Since our measurements are in feet, the length needs to be less than or equal to 22.5 feet.

Alex sells books online. She makes a flat profit of $2.00 per book, but she needs to pay $4.00 per day to Paypal for using the app on her website. How many books does she need to sell to make at least $120.00 per day?

We can multiply the number of books sold by the profit per book and then subtract $4.00 to figure out how much she makes in a day. Let's say b is the number of books Alex sells per day.

2b – 4 = profit each day

Since we want the profit to be at least $120.00, we want it to be greater than or equal to than $120. We can rewrite this as an inequality.

2b – 4 ≥ 120

We solve for b by adding 4 to both sides of the inequality and then dividing by 2.

2b – 4 + 4 ≥ 120 + 4
2b ≥ 124
b ≥ 62

Alex needs to sell at least 62 books per day to make $120.00 , but hopefully she'll sell even more.