Mr. frankel bought 7 tickets to a puppet show and spent $24. he bought a combination of child tickets for $2 each and adult tickets for $4 each. which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought

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10-02-2018
Mathematics

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Mr. frankel bought 7 tickets to a puppet show and spent $24. he bought a combination of child tickets for $2 each and adult tickets for $4 each. which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought

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TheBilogis TheBilogis · Answer 1 · 2018-02-10T07:07:12+01:00

Let x be the number of child tickets he bought
Let y be the number of adult tickers he bought

① x+y=7 (child tickets+adult ticket=7 tickets in total)
② 2x+4y=24 (price of child tickets+price of adult tickets=$24 in total)

We may simply the second equation since all of the coefficients are divisible by 2.

① x+y=7
② x+2y=12

We can now use elimination by multiplying the second equation by -1.

② -(x+2y=12)
② -x-2y=-12

① x+y=7
② -x-2y=-12

Now putting the equations together,
-y=-5
y=5
x=2

Therefore he bought 2 child tickets and 5 adult tickets

keshavgandhi04 keshavgandhi04 · Answer 2 · 2021-12-16T09:27:23+01:00

The total number of adult tickets Mr. Frankel bought is 5 and the total number of child tickets Mr. Frankel bought is 2 and this can be determined by forming the linear equation.

GIven :

Mr. Frankel bought 7 tickets to a puppet show and spent $24.
He bought a combination of child tickets for $2 each and adult tickets for $4 each.

The following steps can be used in order to determine the number of adult tickets, a, and the number of child tickets, c, he bought:

Step 1 - Let the total number of adult tickets be 'a' and let the total number of child tickets be 'c'.

Step 2 - The linear equation that represents the total number of tickets is:

a + c = 7

a = 7 - c --- (1)

Step 3 - The linear equation that represents the total amount he spent on buying tickets is:

4a + 2c = 24 --- (2)

Step 4 - Now, substitute the value of 'a' in the equation (2).

4(7 - c) + 2c = 24

Step 5 - Simplify the above equation.

28 - 4c + 2c = 24

2c = 4

c = 2

Step 6 - Substitute the value of 'c' in equation (1).

a = 7 - 2

a = 5

For more information, refer to the link given below:

https://brainly.com/question/11897796