Suppose a farmer is selling fresh produce at a local farmers market. She sells a quart of strawberries for $3.50 and a head of lettuce for $1.25. She thinks she’ll sell 75 items at most, but she hopes to make at least $150. How many quarts of strawberries and heads of lettuce can she sell to meet her goal?

The farmer must sell at least 25 quarts of berries and 50 heads of lettuce to take in $150 or more for the day.

Step-by-step explanation:

Revenue = (unit cost)(number of units)

The unit cost for quarts of strawberries is $3.50; represent the number of quarts sold by q.

The unit cost for heads of strawberries is $1.25; represent the number of quarts sold by h.

Then q + h = 75 (items); we could solve for q in terms of h, obtaining

q = 75 - h.

Total revenue is then

($3.50/quart)q + ($1.25/h)h ≥ $150

Then 3.50q + 1.25(75 - q) ≥ 150, or

2.25q + 93.75 ≥ 150, or

2.25q               ≥ 56.25

Solving for q, we divide both sides by 2.25, obtaining q ≥ 25.

Since q + h = 75, h = 75 - q, or 75 - 25, or h = 50.

The farmer must sell at least 25 quarts of berries and 50 heads of lettuce to take in $150 or more for the day.

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step-by-step explanation: