Question

1. four hamburgers and two hotdogs cost $42. six hamburgers and five hotdogs cost $75. what is the price of each item? developing

Explanation:

Step1: Define variables for prices

Let $h$ = price of a hamburger, $d$ = price of a hotdog.

Step2: Set up system of equations

$4h + 2d = 42$
$6h + 5d = 75$

Step3: Simplify first equation

Divide first equation by 2: $2h + d = 21$, so $d = 21 - 2h$

Step4: Substitute into second equation

$6h + 5(21 - 2h) = 75$
Expand: $6h + 105 - 10h = 75$
Combine like terms: $-4h + 105 = 75$

Step5: Solve for h

$-4h = 75 - 105$
$-4h = -30$
$h = \frac{-30}{-4} = 7.5$

Step6: Solve for d

$d = 21 - 2(7.5) = 21 - 15 = 6$

Answer:

The price of one hamburger is $\$7.50$, and the price of one hotdog is $\$6.00$.