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At a fruit market where no sales tax is charged, Abe paid ₱1.90 for 1 pear and 3 apples; Joan paid ₱1.60 for 1 pear, 1 apple, and 1 orange; and Latonya paid ₱1.70 for 2 apples and 1 orange. If each person paid the same amount per pear, the same amount per apple, and the same amount per orange, what amount did each person pay for each apple?
let 'x' be the cost of 1 apple 'y' be the cost of 1 pear 'z' be the cost of 1 orange ---------------------------------- Abe paid Php1.90 for 1 pear and 3 apples y + 3x = 1.90 ------equation 1 --------------------------------- Joan paid Php1.60 for 1 pear, 1 apple and 1 orange x + y + z = 1.60 -----equation 2 ------------------------------- Latonya paid Php1.70 for 2 apples and 1 orange 2x + z = 1.70 ----equation 3 --------------------------------- express y and z in terms of x from equation 1 y + 3x = 1.90 y = -3x + 1.90 ----equation 1'
from equation 3 2x + z = 1.70 z = -2x + 1.70 ----equation 3' --------------------------------- Substitute equations 1' and 3' to equation 2 x + y + z = 1.60 x + (-3x + 1.90) + (-2x + 1.70) = 1.60 x - 3x + 1.90 - 2x + 1.70 = 1.60 x - 3x - 2x = 1.60 - 1.70 - 1.90 -4x = -2 x = 0.50 ------------------------------ Substitute x=0.50 to equations 1' and 3' y = -3x + 1.90 y = -3(0.50) + 1.90 y = -1.50 + 1.90 y = 0.40
z = -2x + 1.70 z = -2(0.50) + 1.70 z = -1 + 1.70 z = 0.70 ------------------------------ Therefore apple costs Php0.50 each pear costs Php0.40 each and orange costs Php0.70 each
Lets find the value of x in the first equation x=1.9-3y Lets find the value of z in the third equation. z=1.7-2x z=1.7-3.8+6y z=-2.1+6y Substitute the value on the 2nd equation. 1.9-3y+y-2.1+6y=1.6 4y-0.2=1.6 4y=1.8 y=0.45
Substitute the value of x: x=1.9-3(0.45) x=1.9-1.35 x=0.55
Substitute the value of x z=1.7-2(0.55) z=1.7-1.1 z=0.6
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