Thread: Not sure which branch of mathematics my question relates to. Please help

Hi,

Four friends bought different kind of fruits from the market. When they got home they could not remember the individual prices per kilogram, but 3 if them can remember the total amount that they each paid. The weight of the fruits and the total amount paid are shown as the following:

Pineapple (kgs) Mr A Mr B Mr C Mr D
1.15 kgs 1.20 kgs 2.15 kgs 1.30 kgs


Mangoes (kgs) Mr A Mr B Mr C Mr D
0.60 kgs 0.45 kgs 0.90 kgs 0.25 kgs

Orange (kgs) Mr A Mr B Mr C Mr D
0.55 kgs 0.30 kgs 0.65 kgs 0.50 kgs


Amount paid in ($) Mr A Mr B Mr C Mr D

$8.28 $6.84 $13.05 $ ?

Assuming that for each variety of fruit, the price per kilogram paid by each of the three friends is the same. Calculate the amount which Mr D paid.

Please advise and thank you in advance for the effort

x - cost of 1 kilo pinapple
y - cost of 1 kilo mangoes
z - cost of 1 kilo orange

1.15*x+0.6*y+0.55*z=8.28
1.20*x+0.45*y+0.3*z=6.84
2.15*x+0.9*y+0.65*z=13.05

Now solve the system and find x,y,z so you can calculate the amount which Mr D paid.