Question

Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost? Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations. Let p = the cost of one pear Let a = the cost of one apple
a. Write a system of equations that can be used to determine the cost of pears and apples.
b. Determine the cost of one pear and one apple. Use mathematics to explain how you determined your answer

Answer 1

Answer:

  a. 6p +3a = 3.90; 2p +5a = 3.30

  b. pear: $0.40; apple: $0.50

Step-by-step explanation:

a. The problem statement defines the variables. The relations it describes are ....

  6p +3a = 3.90

  2p +5a = 3.30

__

b. A factor of 3 can be removed from the first equation to give ...

  2p +a = 1.30

Subtracting this from the second equation eliminates the p variable:

  (2p +5a) -(2p +a) = (3.30) -(1.30)

  4a = 2.00

  a = 0.50

Substituting this value into the reduced first equation, we get ...

  2p + 0.50 = 1.30

  p + 0.25 = 0.65 . . . . divide by 2

  p = 0.40 . . . . . . . . . . .subtract 0.25

The cost of one pear is $0.40; the cost of one apple is $0.50.

_____

Comment on the mathematics

The properties of equality allow you to add, subtract, multiply, or divide both sides of the equation by the same number. So when we indicate an operation with a number, we mean "... to both sides of the equation."