SOLUTION: A school tuck shop made 2 orders for large and small pies pies. The first order of 40 small and40 large pies came to $154 and the second order of 50 small and 30 large pies was $14

Question 802970: A school tuck shop made 2 orders for large and small pies pies. The first order of 40 small and40 large pies came to $154 and the second order of 50 small and 30 large pies was $144.50.
A define the variables you will use to solve this question
B form two equations that can be solved simultaneously
C prove the equations
Can you please show me all the workings, I just can't get it..
Thanks
Deanna

Found 2 solutions by Cromlix, thejackal:
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Large pies = x
Small pies = y
40x + 40y = 154........1
30x + 50y = 144.5.......2
Multiply Eq(1) by 3
Multiply Eq(2) by 4
120x + 120y = 462.......3
120x + 200y = 578.......4
Subtract Eq(3) from Eq(4)
80y = 116
y = 116/80
y = 1.45
Substitute y = 1.45 into
Eq.(1).
40x + 40y = 154
40x + 58 = 154
40x = 154 - 58
40x = 96
x = 96/40
x = 2.40
Large pies cost $2.40
Small pies cost $1.45
Hope this helps.
:-)
Answer by thejackal(72) (Show Source): You can put this solution on YOUR website!
very simple
let the unit price of small and large pies be S and L respectively such that
1st order which was - 40S + 40L = $154
2nd order which was - 50S + 30L = $144.50
we want to know what the unit price is for small and large pies, to do this
solve simultaneously
40S + 40L = 154
50S + 30L = 144.50
using either equation, express S in terms of L for example
50S = 144.5 - 30L
S = 2.89 - 3/5L
use the equation for S in the first equation
40 (2.89 - 3/5L) + 40L = 154
simplify
16 L = 38.4
L = 2.4
plug the value of L into the previous equation for S
S = 2.89 - 3/5(2.4)
S = 1.45
prove it by using your answers in the original question
40(1.45) + 40(2.4) should be equal to 154

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