Question

A pound of oranges costs $2 less than a pound of pears. Together, ten pounds of oranges and eight pounds of pears cost $61. How much would three pounds of pears cost?

Answer 1

To determine the cost of three pounds of pears, we solve for the cost per pound of pears given the total cost of a mix of oranges and pears, resulting in $13.50 for three pounds of pears.

Step-by-step explanation:

The student has a math problem involving the cost of oranges and pears where a pound of oranges costs $2 less than a pound of pears. Given the total cost for a certain weight of each fruit, the student needs to determine the cost of a different quantity of pears.

Let's start by designating the cost per pound of pears as P. Therefore, the cost per pound of oranges is P - $2. The equation based on the given details would be: 10(P - $2) + 8P = $61.

To solve for P, we combine like terms and distribute to get 10P - $20 + 8P = $61, which simplifies to 18P = $81. Dividing both sides by 18, we find that P, the cost per pound of pears, is $4.50. Finally, to find out the cost of three pounds of pears, we multiply 3 by the cost per pound: 3 x $4.50 = $13.50.

Therefore, three pounds of pears would cost $13.50.

Answer 2

Let us say that:

o = cost of oranges per pound

p = cost of pears per pound

so that:

o = p – 2

Therefore:

10o + 8p = 61

10 (p – 2) + 8p = 61

10p – 20 + 8p = 61

18p = 81

p = 4.5

p = $4.5 per pound

So 3 pounds of pears would cost:

total cost = 3 * 4.5

total cost = $13.5