Answer: The equations are as follows;
5p + 4d = 43.25 ————(1) and
3p + 2d = 24.25 ————(2)
Also a bag of popcorn costs $5.25
Step-by-step explanation: We start by assigning letters to the unknown variables. Let a bag of popcorn be p and let one drink be d. The clues given in the question include the cost of buying five bags of popcorn and four drinks which is a total of $43.25. This can be expressed as
5p + 4d = 43.25 ————(1)
Another clue is that three bags of popcorn and two drinks cost $24.25. This also can be expressed as
3p + 2d = 24.25 ————(2)
Now we have a pair of simultaneous equations as follows
5p + 4d = 43.25 ————(1)
3p + 2d = 24.25 ————(2)
We shall use the elimination method since all the unknowns have coefficients greater than 1. Multiply equation one by 3, and multiply equation two by 5 (so as to eliminate ‘p’)
5p + 4d = 43.25 ——— x3
3p + 2d = 24.25 ——— x5
15p + 12d = 129.75 ———(3)
15p + 10d = 121.25 ———(4)
Subtract equation (4) from equation (3) and we have
2d = 8.5
Divide both sides of the equation by 2
d = 4.25.
That means each drink costs $4.25
We can now substitute for the value of d into equation (2)
3p + 2d = 24.25
When d = 4.25
3p + 2(4.25) = 24.25
3p + 8.5 = 24.25
Subtract 8.5 from both sides of the equation
3p = 15.75
Divide both sides of the equation by 3
p = 5.25. This means a bag of popcorn costs $5.25
