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denis23 [38]
2 years ago
9

Two movie tickets and three concert tickets cost $21. Three movie tickets and 2 concert tickets cost $19. Each ticket costs a wh

ole number of dollars.
How much does 1 movie ticket cost?
How much does 1 concert ticket cost?
Mathematics
2 answers:
Luden [163]2 years ago
4 0
One concert ticket=5 and one movie ticket=3
Alenkasestr [34]2 years ago
4 0

Answer:

movie ticket = $3 concert = 5$

Step-by-step explanation:

Movie = m Concert = c

2m + 3c = 21

3m + 2c = 19

First find the value of one of the variables by isolating them

3m + 2c = 19

3m = 19 - 2c

m = 19/3 - 2c/3

Input the value for that variable into the other problem

2(19/3 - 2c/3) + 3c = 21

38/3 - 4c/3 + 3c = 21

38/3 + 5c/3 = 21

5c/3 = 21 - 38/3

5c/3 = 63/3 - 38/3

5c/3 = 25/3

5c = 25

c = 5

Now that we've found the actual value for c plug that into any of the 2 problems and solve for m

3m + 2(5) = 19

3m + 10 = 19

3m = 9

m = 3

Movie = 3 Concert = 5

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Answer:

<u>There are two inequalities that represent the total number of </u>

<u>balloons, b, they can purchase and not spend over their budgeted amount:</u>

<u>0.65b ≤ 70</u>

<u>0.65b + 225 ≤ 295</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Budget to plan the event = $ 295

Expenses on supplies so far = $ 225

Cost of each balloon = $ 0.65

2. Which of the following inequalities represents the total number of

balloons, b, they can purchase and not spend over their budgeted amount?

1. Let's find how much of the budget is still available:

Budget available = Budget to plan the event - Expenses on supplies so far

Budget available = 295 - 225

Budget available = $ 70

2. Let's find the inequality that represents the total number of

balloons, b, they can purchase and not spend over their budgeted amount.

Number of balloons ≤ Budget available/Cost of each balloon

Replacing with the values we know, we have:

b ≤ 70/0.65

<u>0.65b ≤ 70</u>

or we can write it also including the total budget this way:

Number of balloons  ≤ Budget to plan the event - Expenses on supplies so far /Cost of each balloon

Replacing with the values we know, we have:

b ≤ (295 - 225)/0.65

0.65b ≤ 295 - 225

<u>0.65b + 225 ≤ 295</u>

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