Answer:
Variable x = $2.39 ⇒ price of 1 pound of cashews
Variable y = $1.79 ⇒ price of 1 pound of peanuts
Step-by-step explanation:
Assume that the price of each pound of cashews is $x and the price of each pound of peanuts is $y
∵ The price of 1 pound of cashews = x
∵ The price of 1 pound of peanuts = y
∵ 5 pounds of cashews and 8 pounds of peanuts cost $26.27
∴ 5x + 8y = 26.27 ⇒ (1)
∵ 7 pounds of cashews and 4 pounds of peanuts cost $23.89
∴ 7x + 4y = 23.89 ⇒ (2)
Now we have a system of equations to solve it
→ Multiply equation (2) by -2 to make the coefficients of y equal
in values and different in signs
∵ -2(7x) + -2(4y) = -2(23.89)
∴ -14x - 8y = -47.78 ⇒ (3)
→ Add equations (1) and (3) to eliminate y
∵ (5x + -14x) + (8y + - 8y) = (26.27 + -47.78)
∴ -9x = -21.51
→ Divide both sides by -9 to find x
∴ x = 2.39
→ Substitute x in equation (1) or (2) to find y
∵ 5(2.39) + 8y = 26.27
∴ 11.95 + 8y = 26.27
→ Subtract 11.95 from both sides
∴ 8y = 14.32
→ Divide both sides by 8 to find y
∴ y = 1.79
∴ The price of 1 pound of cashews is $2.39
∴ The price of 1 pound of peanuts is $1.79
