Answer:
Snickers bar: $0.80
Butterfinger bar: $0.65
Step-by-step explanation:
Let's set up a system of equations to solve for the prices of a Snickers bar (x) and a Butterfinger (y) based on the given information.
Define the Variables:
Let:
Translate the Given Information into Equations:
We have two pieces of information from the problem:
Therefore, we can write two equations based on these facts:
Equation 1: Total Cost
[tex] 9x + 6y = 11.10 [/tex]
Equation 2: Price Difference
[tex] x - y = 0.15 [/tex]
[tex] x = y + 0.15 [/tex]
Substitute Equation 2 into Equation 1:
Substitute x = y + 0.15 from Equation 2 into Equation 1:
[tex] 9(y + 0.15) + 6y = 11.10 [/tex]
Simplify and Solve for y:
Expand and simplify the equation:
[tex] 9y + 1.35 + 6y = 11.10 [/tex]
[tex] 15y + 1.35 = 11.10 [/tex]
Subtract 1.35 from both sides:
[tex] 15y = 11.10 - 1.35 [/tex]
[tex] 15y = 9.75 [/tex]
Divide both sides by 15 to solve for y:
[tex] y = \dfrac{9.75}{15} [/tex]
[tex] y = 0.65 [/tex]
Find x Using y:
Substitute y = 0.65 back into Equation 2 to solve for x:
[tex] x = 0.65 + 0.15 [/tex]
[tex] x = 0.80 [/tex]
Conclusion:
Therefore, the price of a Snickers bar (x) is [tex]\boxed{0.80} [/tex] dollars, and the price of a Butterfinger bar (y) is [tex]\boxed{0.65}[/tex] dollars.
Hence, a Snickers bar costs $0.80, and a Butterfinger bar costs $0.65.
