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For a school play, Rico bought 3 adult tickets and 5 child tickets for $40. Sasha bought 1 adult ticket and 5 child tickets for $25. Find the cost of an adult ticket and the cost of a child ticket. Then find how much Julia will pay for 5 adult tickets and 3 child tickets

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absor201

The cost of one adult ticket is $7.5 and one child ticket is $3.5

Julia will pay $48 for 5 adult tickets and 3 child tickets.

Step-by-step explanation:

Let,

Cost of one adult ticket = x

Cost of one child ticket = y

According to given statement;

3x+5y=40    Eqn 1

x+5y=25      Eqn 2

Subtracting Eqn 2 from Eqn 1

[tex](3x+5y)-(x+5y)=40-25\\3x+5y-x-5y=15\\2x=15[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{15}{2}\\x=7.5[/tex]

Putting x=2.5 in Eqn 1

[tex]3(7.5)+5y=40\\22.5+5y=40\\5y=40-22.5\\5y=17.5[/tex]

Dividing both sides by 5

[tex]\frac{5y}{5}=\frac{17.5}{5}\\y=3.5[/tex]

The cost of one adult ticket is $7.5 and one child ticket is $3.5

5 adult tickets = 5*7.5 = $37.5

3 child tickets = 3*3.5 = $10.5

Total = 37.5+10.5 =$48

Julia will pay $48 for 5 adult tickets and 3 child tickets.

Keywords: linear equation, subtraction

Learn more about subtraction at:

  • brainly.com/question/3071107
  • brainly.com/question/3126500

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Lanuel

a. The cost of an adult ticket is equal to $7.5.

b. The cost of an child ticket is equal to $3.5.

c. Ju-lia will pay $48 for 5 adult tickets and 3 child tickets.

  • Let the cost of a child ticket be b.
  • Let the cost of an adult ticket be a.

Given the following data:

  • Rico's expenses = $40.
  • Sasha's expenses = $25.

Translating the word problem into an algebraic expression, we have;

For Rico:

[tex]3a + 5c =40[/tex]   ....equation 1.

For Sasha:

[tex]a + 5c=25[/tex]   ....equation 2.

Making a the subject of formula in eqn. 2, we have:

[tex]a=25-5c[/tex]   ....equation 3.

Substituting eqn. 3 into eqn. 1, we have:

[tex]3(25-5c)+5c=40\\\\75-15c+5c=40\\\\35=10c\\\\c=\frac{35}{10}[/tex]

c = $3.5

For the value of a:

[tex]a=25-5c\\\\a=25-5(3.5)\\\\a=25-17.5[/tex]

a = $7.5

c. Cost of 5 adult tickets and 3 child tickets:

[tex]5a + 3c\\\\5(7.5)+ 3(3.5) = 37.5 + 10.5\\\\5a + 3c = 48[/tex]

Therefore, Ju-lia will pay $48 for 5 adult tickets and 3 child tickets.

Find more information: https://brainly.com/question/596290

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