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18 votes
18 votes
A store sells bags that contain tubes of lip balm and travel size lotions. A bag that has 2 tubes of lip balm and 3 lotions costs $21. A bag that has 3 tubes of lip balm and 4 lotions costs $29. How much would a bag that has 5 tubes of lip balm and 5 lotions cost?

User Glenn Strycker
by
2.8k points

2 Answers

19 votes
19 votes

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

User Rishy
by
3.0k points
16 votes
16 votes

Answer:

$43

Step-by-step explanation:

b = lip balm

L = lotion

2b + 3L = 21

3b + 4L = 29

3(2b + 3L = 21)

-2(3b + 4L = 29)

6b + 9L = 63

-6b - 8L = -58

L = 5

2b + 3(5) = 21

2b + 15 = 21

2b = 6

b = 3

5b + 5L = ?

5(3) + 5(5)

18 + 25

= 43

User James Wright
by
3.1k points