2 peaches and 12 apples cost $14.60. 6 peaches and 4 apples cost $18.20. How much is an peach?

Answer 1

Let us assume peach be x and apples be y

therefore the equations we have,

2x + 12y = 14.60 --------------------- (1)

6x + 4y = 18.20 --------------------- (2)

Transforming the first equation,

2x + 12y = 14.60

2x = 14.60 - 12y

x = (14.60 - 12y) / 2 -------------------- (3)

Using (3), and evaluating in equation (2), we get

6x + 4y = 18.20

6 * (14.60 - 12y) / 2 + 4y = 18.20

y = 0.8 -------------------- (4)

Now using (4) and substituting the value in equation (3),

x = (14.60 - 12(0.8)) / 2

x = 2.5

Hence, the value of a peach is $ 2.5 while that of an apple is $ 0.8

Answer 2

Easier to avoid fraction if transform 1st equation to eliminate the x term.

2x + 12y = 14.60

6x + 4y = 18.20 Mult 1st by -3

-6x - 36y = - 43.80

6x + 4y = 18.20 Add them

-32y = 25.60 y = $0.80

2x + 12(0.80) = 14.60

2x = 14.60 - .9.6 ; 2x = 5 x = $2.50 (an expensive peach!)

Another suggestion or two: Check answer by substituting the results into one (or both) of the original equations to see if it balances and why not use A for apples and P for peaches to keep track of which variable is which.