A fruit market must spend less than $350 for an order of peaches and mangoes. A pound of peaches costs $0.50 and a pound of mangoes costs $1.75. This relationship is shown in the graph. The market needs at least 50 more pounds of peaches than mangoes. Which choice is a reasonable solution?
500 pounds of peaches and 100 pounds of mangoes
200 pounds of peaches and 150 pounds of mangoes
200 pounds of peaches and 100 pounds of mangoes
50 pounds of peaches and 100 pounds of mangoes
To find a reasonable solution, we need to check each option against the two conditions: the total cost must be less than $350, and there must be at least 50 more pounds of peaches than mangoes.
1. Cost Calculation: The cost can be calculated as:
[
text{Total Cost} = (text{pounds of peaches} times 0.50) + (text{pounds of mangoes} times 1.75)
]
2. Peach and Mango Relationship: The requirement is that the pounds of peaches (P) must be at least 50 more than the pounds of mangoes (M):
[
P geq M + 50
]
Now, let’s evaluate each option:
1. 500 pounds of peaches and 100 pounds of mangoes:
– Cost = (500 * 0.50) + (100 * 1.75) = 250 + 175 = 425 (not less than $350)
– Relationship: 500 ≥ 100 + 50 (true)
2. 200 pounds of peaches and 150 pounds of mangoes:
– Cost = (200 * 0.50) + (150 * 1.75) = 100 + 262.5 = 362.5 (not less than $350)
– Relationship: 200 ≥ 150 +