Question

Two groups of people order food at a restaurant. One group orders 4 hamburgers and 7 chicken sandwiches for $34.50. The other group orders 8 hamburgers and 3 chicken sandwiches for $30.50. Find the cost of each item. Write and solve in an system of equations using elimination

Answer 1

Assuming h stands for hamburgers and s stands for chicken sandwiches, then we can represent the statement like so:
$4h + 7s = 34.5 \\ 8h + 12s = 30.5$
Using Elimination method:
Multiply the first equation by 8 and multiply
the second equation by 4
$(8 \times 4h) + (8 \times 7s) = (8 \times 34.5) \\ (4 \times 8h) + (4 \times 3s) = (4 \times 30.5)$
Simplify
$32h + 56s = 276 \\ 32h + 12s = 122$

Subtract equation 2 from 1
$32h + 56s = 276 \\ - \\ 32h + 12s = 122$
$44s = 154$
Simplify further by dividing both sides by the coefficient of s
$s = \frac{154}{44}$
$hence \: s = 3.5 \: dollars$
Substitute for s in equation 1
$4h + 7(3.5) = 34.5$

$4h + 24.5 = 34.5$

Collect like terms
$4h = 34.5 - 24.5$
$4h = 10$
$h = \frac{10}{4}$
$h = 2.5 \: dollars$
Hence, the cost of hamburgers is $2.5 and chicken sandwiches is $3.5