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:
[tex]5L+3G=163[/tex]
In the second statement Marie received an order of 4 trays of lasagna and 4 trays of garlic bread and so:
[tex]4L+4G=150.80[/tex]
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:
[tex]4(5L+3G=163)\\20L+12G=652[/tex]
Equation 2:
[tex]3(4L+4G=150.80)\\12L+12G=452.40[/tex]
Now we can subtract equation 2 from equation 1 and eliminate the "G" variable as such:
[tex]20L+12G=652\\-(12L+12G=452.40)\\\\8L+0G=199.60\\\\8L=199.60\\\\[/tex]
By solving for L we obtain:
[tex]8L=199.60\\\\\frac{8L}{8}=\frac{199.60}{8}\\\\L=24.95[/tex]
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:
[tex]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[/tex]
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~~~
