Question

WHY CAN'T ANYONE HELP ME? :( Jen Butler has been pricing​ Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $106. Two adults and three children must pay $75. Find the price of the​ adult's ticket and the price of a​ child's ticket.

Answer 1

Children: $13

Adults: $18

Explanation:

Well for both sets we can set up the following system of equations,

`\left \{ {{3a + 4c = 106} \atop {2a + 3c = 75}} \right.`

So first we need to solve for a in the first equation.

3a + 4c = 106

-4c to both sides

3a = -4c + 106

Divide 3 by both sides

a = -4/3c + 35 1/3

Now we plug in that a for a in 2a + 3c = 75.

2(-4/3c + 35 1/3) + 3c = 75

-8/3c + 70 2/3 + 3c = 75

Combine like terms

1/3c + 70 2/3 = 75

-70 2/3 to both sides

1/3c = 4 1/3

Divide 1/3 to both sides

c = 13

Now we can plug in 13 for c in 3a + 4c = 106,

3a + 4(13) = 106

3a + 52 = 106

-52 to both sides

3a = 54

Divide 3 by both sides.

a = 18

Thus,

an adult ticket is $18 and a children's ticket is $13.

Hope this helps :)

Answer 2

Adults pay $18 and children pay $13.5

Explanation:

Hello!

You need to calculate the price of the tickets for adults and children for the group trip to New York.

If X represents adult and Y represents children, then you can express the given information as two equations with two unknown values:

Three adults and four children must pay $106. ⇒ 3X + 4Y= $106

Two adults and three children must pay $75. ⇒ 2X + 3Y= $75

I) First step, in one of the equations you have to clear one of the unknown values, I'll clear the value of Y:

3X + 4Y= 106

4Y= 106 - 3X

`Y= (106-3X)/(4)`

II) Second step you have to replace it in the second equation:

2X + 3Y= 75

`2X + 3((106-3X)/(4) )= 75`

`2X + (3)/(4)(106-3X)= 75`

`2X + ((3)/(4)*106 - (3)/(4)*3X )= 75`

`2X + 79.5 -(9)/(4)X =75`

`2X - (9)/(4)X= 75 - 79.5`

`-(1)/(4) X= -(9)/(2)`

`X= -(9)/(2) * -4= 18`

The price for adult tickets is $18.

III) Third step, using the calculated value of X, you replace it on the formula obtained in I) yo calculate the price for the children Y:

`Y= (106-3X)/(4)= (106-(3*18))/(4) = (27)/(2)= 13.5`

The ticket price for children is $13.5

I hope this helps!