Question

Four tins of soup and 3 packs of bread rolls cost $10:80.

Two tins of soup and 5 packs of bread rolls cost $9:60.
Find the cost of 3 tins of soup and 7 packs of bread rolls.​

Answer 1

$13.80

Explanation:

Let x be cost of 1 tin of soup and y be the cost of 1 pack of bread roll

We get two equations for each of the situations described

1. four tins of soup and 3 packs of bread rolls cost $10:80

==> 4x + 3y = 10.80 (1)

2. Two tins of soup and 5 packs of bread rolls cost $9:60

==> 2x + 5y = 9.60 (2)

Multiply equation (2) by 2:
2(2x + 5y) = 2 x 9.60
4x + 10y = 19.20 (3)

Subtract Equation (1) from Equation (3) to eliminate 4x terms
(3) - (1)

==> (4x + 10y) - (4x + 3y) = 19.20 - 10.80

==> 4x - 4x + 10y - 3y = 8.40

==> 7y = 8.40

==> y = 8.40/7 = 1.20

Substitute y = 1.20 in equation (2):
2x + 5(1.20) = 9.60

2x + 6 = 9.60

2x = 9.60 - 6

2x = 3.60

x = 3.60/2 = 1.80

So 1 tin of soup costs $1.80 and 1 bread roll costs $1.20

Cost of 3 tins of soup and 7 bread rolls

= 3 x 1.80 + 7 x 1.20

= 5.40 + 8.40

= $13.80

Answer 2

$13.80

Explanation:

Given the following costs, you want the cost of 3 soup tins and 7 bread packs.

• 4 soup tins + 3 bread packs = $10.80
• 2 soup tins + 5 bread packs = $9.60

Cost of each

Subtracting the first equation from twice the second gives ...

2(2s +5b) -(4s +3b) = 2(9.60) -(10.80)

7b = 8.40 . . . . . simplify

b = 1.20 . . . . . . . divide by 7

Solving for s in the second equation, we have ...

2s +5(1.20) = 9.60

2s = 3.60 . . . . . . subtract 6.00

s = 1.80 . . . . . . . . divide by 2

Purchase cost

Then the cost of 3 soup tins and 7 bread packs is ...

3(1.80) +7(1.20) = 5.40 +8.40 = 13.80

The cost of 3 tins of soup and 7 packs of bread rolls is $13.80.