help with my homework

Question

Duane and Eli are buying snacks. Duane spends $18.25 on two bags of popcorn and three drinks. Eli spends $27.50 on four bags of popcorn and two drinks. Let x = the cost of one bag of popcorn Let y = the cost of one drink

A. Write a system of equations that can be used to find the cost of one bag of popcorn and one drink

B. Use the system of equations to algebraically determine the cost of a bag of popcorn and the cost of one drink to the nearest cent.

Answer 1

For Duane:

2x + 3y = 18.25 (imagine the cost of a bag of popcorn was $1 and one drink $2, then Duane would spend 2(1)+3(2) or $8)--x and y are representing the unknown cost for each item.

For Eli:

4x + 2y = 27.50

Now how to solve that system for x and y? Substitution or addition/elimination? (there are other methods too, but those come later)

If you use addition/elimination, notice that multiplying Duane's equation by -2 then adding the result to Eli's equation has the effect of eliminating the variable y.

-4x - 6y = -36.50 (Duane's multiplied by -2, using multiplication property for equality)

4x + 2y = 27.50 (Eli's repeated)

0 -4y = -9.00 ( equals added to equals are equal)

y = 2.25

To find x, substitute for y and solve for x in any of the above equations:

2x+3(2.25)=18.25

2x+6.75= 18.25

2x = 11.50

x=5.75

Take a look on Desmos for verification:

desmos.com/calculator/t5hqro8yco

Select the desmos url above, right click, and choose "go to...".