Final answer:
A piece of fudge costs $1.05 and a piece of bubble gum costs $0.15. Two equations were set up from the given purchases and solved using the elimination method to find the cost of each item. The options provided in the question do not match these results.
Step-by-step explanation:
The question asks us to determine the cost of a piece of fudge and a piece of bubble gum based on the given information. We can set up two equations to solve for the price of each item using variables. Let's assume the price of fudge is represented by 'f' and the price of bubble gum is represented by 'g'.
Kalice's purchase: 5f + 3g = $5.70 (Equation 1)
Yasmeen's purchase: 2f + 10g = $3.60 (Equation 2)
We can solve these equations using the substitution or elimination method. Let's multiply Equation 2 by 2.5 to align the fudge terms with Equation 1:
- 2.5(2f + 10g) = 2.5($3.60)
- 5f + 25g = $9.00 (Equation 3)
Now subtract Equation 1 from Equation 3:
- (5f + 25g) - (5f + 3g) = $9.00 - $5.70
- 22g = $3.30
- g = $3.30 / 22
- g = $0.15 (price of one piece of bubble gum)
Plug the value of 'g' into Equation 1 to find the price of fudge:
- 5f + 3($0.15) = $5.70
- 5f + $0.45 = $5.70
- 5f = $5.70 - $0.45
- 5f = $5.25
- f = $5.25 / 5
- f = $1.05 (price of one piece of fudge)
Therefore, a piece of fudge costs $1.05 and a piece of bubble gum costs $0.15. However, the options provided do not match these calculations, so we might need to check the calculations again or inform the student of a possible error in the options.