Final answer:
One piece of bubble gum costs $0.15 and one piece of fudge costs $1.05.
Step-by-step explanation:
Let's assign variables to the cost of one piece of fudge and one piece of bubble gum.
Let x be the cost of one piece of fudge.
Let y be the cost of one piece of bubble gum.
We can use these variables to set up two equations based on the information given.
From the first sentence, we know that Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. This can be represented as the equation:
5x + 3y = 5.70
From the second sentence, we know that Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. This can be represented as the equation:
2x + 10y = 3.60
We now have a system of two equations with two variables. We can solve this system to find the values of x and y, which represent the cost of one piece of fudge and one piece of bubble gum.
Step 1: Multiply both sides of the first equation by 2 and the second equation by 5 to eliminate x:
10x + 6y = 11.40
10x + 50y = 18.00
Step 2: Subtract the first equation from the second equation to eliminate x:
10x + 50y - (10x + 6y) = 18.00 - 11.40
44y = 6.60
Step 3: Divide both sides of the equation by 44 to solve for y:
y = 6.60 / 44 = 0.15
Therefore, one piece of bubble gum costs $0.15.
Step 4: Substitute the value of y into one of the original equations. Let's use the first equation:
5x + 3(0.15) = 5.70
5x + 0.45 = 5.70
5x = 5.70 - 0.45 = 5.25
x = 5.25 / 5 = 1.05
Therefore, one piece of fudge costs $1.05.