Question

How to do this question plz ​

Answer 1

Adult ticket= $7

Child Ticker=$2

Explanation:

Family 1: 2x+3y=20

Family 2: x+4y=15

2x+3y=20

x+4y=15

Multiply by 2

2x+3y=20

-(2x+8y=30)

Change the signs

2x+3y=20

-2x-8y=-30

Eliminate x

-5y=-10

Divide both sides by -5

y=2<---- Price per children

Substitute the value of y

x+4(2)=15

x+8=15

x=15-8

x=7 <----Price per adult

Check:

Substitute the values of x and y to family 1

2(7)+3(2)=20

14+6=20

20=20

7+4(2)=15

7+8=15

15=15

Answer 2

An adult ticket costs £7.

A child ticket costs £2.

Explanation:

Let a represent the cost for adults and let c represent the cost for children.

Family 1 has a total of 2 adults and 3 children. Together, it cost them £20.

In an equation, this is:

`2a+3c=20`

Family 2 has a total of 1 adult and 4 children. It cost them £15. In an equation, this is:

`a+4c=15`

We know have a system of equations. Solve it. We can use the substitution method.

First, subtract both sides by 4c in the second equation:

`a+4c=15\\a=15-4c`

Substitute this into the first equation:

`2a+3c=20\\2(15-4c)+3c=20`

Distribute:

`30-8c+3c=20`

Add:

`30-5c=20`

Subtract 30 from both sides. The left cancels:

`-5c=-10`

Divide both sides by -5:

`(-5c)/-5=(-10)/-5\\c=2`

Thus, the cost of a child ticket is £2.

Substitute 2 for c into the equation we manipulated at the start:

`a=15-4c\\a=15-4(2)\\a=15-8=7`

Thus, the cost of an adult ticket is £7.