Inequalities Graphs and Word Problems

In order to make some extra money, Justin is mowing lawns.  He charges $11 to mow a small lawn and $26 to mow a large lawn.  He would like to make at least $130.
Write an inequality that describes the situation.
Let x = # of small lawns mowed
Let y = # of large lawns mowed

• 11x + 26y ≥ 130

• 11x + 26y ≤ 130

• 11x + 26y > 130

• 11x + 26y < 130

Janel bought three apples and two oranges. The total amount she paid was at most $123. If x represents the number of apples and y the number of oranges, which of the following mathematical statements represents the given situation?

Triniti had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Which inequality represents her situation?

• 200 + 25x ≥ 500

• 500 + 25x ≥ 200

• 500 - 25x ≥ 200

• 500 - 25x ≤ 200

A willow tree is 5.1 feet tall and grows at a rate of 2.5 feet a year. After how many years will the tree have reached no more than 60 feet tall?

• 5.1 + 2.5y ≥ 60

• 60 < 5.1 + 2.5

• 5.1 + 2.5y ≤ 60

• 5.1 + 2.5y > 60

Carolyn bought a dress that cost $45 and several pairs of pants, p, that were $9.99 each.  Michelle bought a jacket for $30 and pants that cost $11.50 each.  How many pairs of pants would the girls have to buy for Michelle’s total to exceed Carolyn’s total?

• 45 + 30 > 9.99p + 11.50p 

• 45p + 9.99 > 30p + 11.50

• 45 + 9.99p < 30 + 11.50p

• 45 + 9.99p > 30 + 11.50p

Which point below is NOT part of the solution set?

• (0, 0)

• (5, 1)

• (-1, -3)

• (20, -5)

Which of the following equations match the given graph?

• y ≤ -3/4 x + 3

• y ≥ -3/4 x + 3

• y < -3/4 x + 3

• y > -3/4 x + 3

Which of the following equations match the given graph?

• y ≥ -3x + 4

• y ≤ 3/5x - 5

• y > -x - 5

• y < -4

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Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• 10x + 1.50 ≥ 40

• 1.50x + 10 ≤ 40

• 1.50x + 10 <40

• 10x + 1.50 < 40