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Igoryamba
3 years ago
14

Bill's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 5 adult tickets and 14 st

udent tickets for a total of $198. The school took in $156 on the second day by selling 10 adult tickets and 8 student tickets. Find the price of an adult ticket and the price of a student ticket.
Mathematics
1 answer:
wariber [46]3 years ago
8 0

Answer: The price of an adult ticket = $6

The price of a student ticket = $12

Step-by-step explanation:

Let the price of an adult ticket be a

Let the price of a student ticket be b.

From the question,

5a + 14b = 198 ...... equation i

10a + 8b = 156....... equation ii

Multiply equation i by 10

Multiply equation ii by 5

50a + 140b = 1980 ...... equation iii

50a + 40b = 780 ....... equation iv

Subtract iv from iii

100b = 1200

b = 1200/100

b = 12

Put the value of b into equation ii

10a + 8b = 156

10a + 8(12) = 156

10a + 96 = 156

10a = 156-96

10a = 60

a = 6

The price of an adult ticket = $6

The price of a student ticket = $12

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If 541 people use the swimming pool and children pay 1.75 dollars and adults pay 2.25 and in total earned was 1041.25 how many c
Zina [86]

Answer:

352 children

Step-by-step explanation:

Solve algebraically using a system of equations

Assign variables

let "a" be the number of adults

let "c" be the number of children    <-- We want to find this

a + c = 541             Equation for number of people

2.25a + 1.75c = 1041.25           Equation for money

<u>Rearrange the equation for people</u>. Isolate the variable you don't want to find.

a = 541 - c

<u>Substitute</u> "541 - c", replacing "a", in the equation for money

2.25a + 1.75c = 1041.25              

2.25(541 - c) + 1.75c = 1041.25               Distribute over brackets

1217.25 - 2.25c + 1.75c = 1041.25               Collect like terms

1217.25 - 0.5c = 1041.25                   Simplified equation

<u>Start isolating "c".</u> Move anything that's not "c" to the right side. Move numbers in reverse BEDMAS order. That means we will add/subtract before dividng/multiplying. When moving a number, do its reverse operation to the entire equation.

1217.25 - 0.5c = 1041.25      Do the reverse of positive 1217.25

1217.25 - 1217.25 - 0.5c = 1041.25 - 1217.25    Subtract 1217.25 on both sides  

-0.5c = -176               Do the reverse of multiplying by -0.5

-0.5c/-0.5 = -176/-0.5               Divide both sides by -0.5

c = 352                Number of children

Therefore, there were 352 children in the pool.

5 0
3 years ago
Jason owns a small textile company that produces shirts. On a particular day, Jason has one worker come into the shop to make sh
Vesna [10]

Answer:

Variables:

x → The number of hours the worker worked

y → The number of shirts the worker made.

System fo equations:

\left \{ {{25x+1.75 y=270} \atop {y=5x}} \right.

Step-by-step explanation:

Let be x the number of hours the worker worked and y the number of shirts the worker made.

Since:

  • Jason must pay the worker $25 per hour (which can be represented with 25x).
  • He must pay $1.75 per shirt for material costs (which can be represented with 1.75y).
  • The total expenses were $270.

You can write the following equation:

25x+1.75 y=270

Knowing that the worker created an average of 5 shirts per hour, you can write the other equation:

y=5x

Therefore, with this equations you can set up the following system of equations, which could be used to determine the number of hours the worker worked and the number of shirts the worker made:

\left \{ {{25x+1.75 y=270} \atop {y=5x}} \right.

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3 years ago
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LekaFEV [45]

Answer:

The distance between C and D is 6 units

6 0
3 years ago
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