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
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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.
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<em>Comment on the mathematics</em>
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."