Final answer:
To calculate the cost of a bag with 5 tubes of lip balm and 5 lotions, we establish the prices for a single tube of lip balm and a single lotion by creating a system of linear equations from the information provided. After finding the individual costs, we multiply these by 5 to get the total cost of the desired bag.
Step-by-step explanation:
To solve the problem of how much a bag with 5 tubes of lip balm and 5 lotions would cost, we need to establish the cost of a single tube of lip balm and a single lotion. We can do this by setting up a system of equations based on the information given about the other bags.
Let B represent the cost of a tube of lip balm, and let L represent the cost of a lotion. We are given that:
2B + 3L = $21 (for the first bag)
3B + 4L = $29 (for the second bag)
Now we solve this system of equations to find B and L.
Step 1: Solve the first equation for L
L = ($21 - 2B) / 3
Step 2: Substitute L in the second equation
3B + 4(($21 - 2B) / 3) = $29
Step 3: Solve for B
After simplifying the equation, we find the value of B.
Step 4: Substitute B back into the first equation to find L
Using the value of B, we substitute it back into the first equation to solve for L.
Step 5: Calculate cost of the desired bag
Once we have B and L, we calculate the cost for 5 tubes of lip balm and 5 lotions.
(5B) + (5L) = Cost of the desired bag