Answer:
The large box weighs 18.75 and the small box weights 15.75
Step-by-step explanation:
We are looking to find 2 variables so we will need two equations.
Let l = the large box weight
Let s = the small box weight
7l + 9s + 273 5l +3s = 141
I want to add these two equations together and have one of the variables be eliminated. The way both equations are written now, neither variable will drop out. I see that 9 is a multiple of 3. If I multiply the second equation all the way through by - 3, the s variable will be eliminated.
-3(5l +3s) -3(141) Multiple everything by -3
-15l -9s = -423 Now I will add this to the original equation 7l + 9s = 273
7l + 9s = 273
-8l = -150 Divide both sides by -8
l = 18.75 This is the weight of the large box.
Plug in 18.75 to either of the ordinal equations to find the weight of the small box.
5l + 3s = 141
5(18.75) + 3s = 141 Distribute the 5
93.75 + 3s = 141 Subtract 93.75 from both sides
3s = 47.25 Divide both sides by 3
s = 15.75
Check:
Plug in 15.75 for s and 18.75 for l into both of the original equation to see if they equal.
7l + 9s = 273
7(18.75) + 9(15.75) =273
131.25 + 141.75 = 273 Checks
5l + 3s = 141
5(18.75) + 3(15.75) = 141
93.75 + 47.25 = 141
141 = 141 Checks
