Kathy works at an optical store selling eyeglasses. Each week she earns $180 plus a 2% commission of her total sales for the week. Next week she wants to earn at least $350.
1. Write an inequality that represents the dollar amount of eyeglasses kathy must sell to earn at least $350
2. What dollar amount of eyeglasses must kathy sell to reach her goal of earning $350?
3. If the average cost of a pair of eyeglasses is $250, how many pairs of eyeglasses must she sell?
Let x = amount of sales
1. 180 + .02x ≥ 350
2. Solve for x.
3. x/250 = ?
1. The inequality that represents the dollar amount of eyeglasses Kathy must sell to earn at least $350 can be written as:
180 + 0.02x ≥ 350, where x represents the total sales for the week (in dollars).
2. To find the dollar amount of eyeglasses Kathy must sell to reach her goal of earning $350, we need to solve the inequality:
180 + 0.02x ≥ 350.
First, subtract 180 from both sides of the inequality:
0.02x ≥ 170.
Next, divide both sides of the inequality by 0.02:
x ≥ 8500.
Therefore, Kathy must sell at least $8500 worth of eyeglasses to reach her goal of earning $350.
3. If the average cost of a pair of eyeglasses is $250, to determine how many pairs of eyeglasses she must sell, divide the total sales amount by the cost per pair:
x = 8500 / 250.
Simplifying the expression, we find:
x = 34.
Therefore, Kathy must sell 34 pairs of eyeglasses to reach her goal of earning $350 if the average cost per pair is $250.
1. To write an inequality that represents the dollar amount of eyeglasses Kathy must sell to earn at least $350, we can use the following expression:
180 + 0.02x ≥ 350
Here, x represents the total sales for the week and 0.02x represents the 2% commission Kathy earns on her sales. The inequality states that the sum of her base pay ($180) and her commission must be greater than or equal to $350.
2. To find the dollar amount of eyeglasses Kathy must sell to reach her goal of earning $350, we can solve the inequality:
180 + 0.02x ≥ 350
First, we can subtract 180 from both sides to isolate 0.02x:
0.02x ≥ 350 - 180
0.02x ≥ 170
Next, we divide both sides by 0.02 to solve for x:
x ≥ 170 / 0.02
x ≥ 8500
Therefore, Kathy must sell at least $8,500 worth of eyeglasses to earn at least $350.
3. If the average cost of a pair of eyeglasses is $250, we can find out how many pairs Kathy must sell by dividing the total sales required by the average cost per pair:
Total sales = $8,500
Average cost per pair = $250
Number of pairs = Total sales / Average cost per pair
Number of pairs = $8,500 / $250
Number of pairs = 34
Therefore, Kathy must sell at least 34 pairs of eyeglasses to reach her goal of earning $350, assuming the average cost per pair is $250.