Question

Marie placed two orders at the same restaurant last month. In one order, she received 5 trays of lasagna and 3 trays of garlic bread for $163. In the other order, she received 4 trays of lasagna and 4 trays of garlic bread for $150.80. What is the price for one tray of lasagna, l, and one tray of garlic bread, g? l = $24.95 g = $12.75 l = $12.75 g = $24.95 l = $24.75 g = $12.95 l = $12.95 g = $24.75

Answer 1

Answer:

L=$24.95 , G=$12.75

Step-by-step explanation:

This problem is a classic system of equations problem.  There are several methods of solving these problems, because of the circumstances and values given I think it's best to use the elimination method.  The elimination method attempts to cancel out a variable by subtracting one equation from another.  

The first statement Marie received an order of 5 trays of lasagna and 3 trays of garlic bread for a total of $163.  I'm going to use "L" for lasagna and "G" for garlic bread.  Therefore, the equation for the scenario above is:

$5L+3G=163$

In the second statement Marie received an order of 4 trays of lasagna and 4 trays of garlic bread and so:

$4L+4G=150.80$

Now we cannot use the elimination method directly because equation 1 and equation 2 do not have any coefficients in common.  However, we can eliminate "G" by first multiplying the top equation by 4 and the bottom equation by 3.  We are doing this because those are the coefficients of the other equation, and thus will return a common value as such:

Equation 1:

$4(5L+3G=163)\\20L+12G=652$

Equation 2:

$3(4L+4G=150.80)\\12L+12G=452.40$

Now we can subtract equation 2 from equation 1 and eliminate the "G" variable as such:

$20L+12G=652\\-(12L+12G=452.40)\\\\8L+0G=199.60\\\\8L=199.60$

By solving for L we obtain:

$8L=199.60\\\\\frac{8L}{8}=\frac{199.60}{8}\\\\L=24.95$

Therefore, one tray of lasagna is $24.95.  Now that we know the value of "L" we can use any of our original equations to figure out what "G" is.  I'll use the first equation and so:

$5L+3G=163\\\\5(24.95)+3G=163\\\\124.75+3G=163\\\\124.75-124.75+3G=163-124.75\\\\3G=38.25\\\\\frac{3G}{3}=\frac{38.25}{3}\\\\G=12.75$

And so the price of a tray of garlic bread is $12.75.  So the answer is the price of lasagna = $24.95  and garlic bread = $12.75

~~~Brainliest Appriciated~~~