Final answer:
To find the price of a bag of chips and a candy bar, a system of equations based on the purchases is set up and solved using the method of elimination or substitution, resulting in a bag of chips costing $3 and a candy bar costing $2.
Step-by-step explanation:
We have two scenarios involving purchasing a bag of chips and candy bars, with different quantities and total prices. To find the price of one bag of chips and one candy bar, we need to set up a system of equations based on the information provided:
- Ana paid $11 for one bag of chips and four candy bars.
- Dan paid $16 for two bags of chips and five candy bars.
Let C represent the cost of a bag of chips and B represent the cost of a candy bar. We can then create the following equations:
- C + 4B = $11
- 2C + 5B = $16
To solve for C and B, we can use the method of substitution or elimination. If we multiply the first equation by 2, we have 2C + 8B = $22, which we can subtract from the second equation to find the cost of a candy bar. Subsequently, we can substitute the value of B into either equation to find the cost of a bag of chips.
By solving the equations, we find that a bag of chips costs $3 and a candy bar costs $2.