Question

CAN ANYONE HELP ME PLEASE? 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

Answer:

adult=18$ and children=13$

Step-by-step explanation:

a= adult. and. c= children

first change the statement into linear equation

3a+4c=106

2a+3c=75

then it just solving for a and y

3a+4c=106. a= 75-3c.

2

3(75-3c)+ 4c=106. solve for c

2

c=13

then find c by substituting the value you got into a . you can you either 3a+4c=106

or 2a+3c=75 to find the answer but the value of a is the same.

2a+3c=75. c=13

2a+3(13)=75

2a=75 -39

2a= 36

a=18

Answer 2

Answer:

Adults Ticket = $18

Child's Ticket = $13

Step-by-step explanation:

Let A denote the price of an adult's ticket

Let C denote the price of a child's ticket

It is given that the three adults and four children must pay $106.

Mathematically,

$3A + 4C = 106 \:\:\:\:\:\:\:\:\:\:\: eq. 1$

It is also given that the two adults and three children must pay $75.

Mathematically,

$2A + 3C = 75 \\\\2A = 75 - 3C$

$A = \frac{(75 - 3C)}{2} \:\:\:\:\:\:\: eq\:. 2$

Substitute eq. 2 into eq. 1

$3A + 4C = 106$

$\frac{3(75 - 3C)}{2} + 4C = 106$

Simplify,

$\frac{3(75 - 3C)}{2} + 4C = 106$

$\frac{225 - 9C}{2} + 4C = 106$

$\frac{225 - 9C + 2(4C)}{2} = 106$

$\frac{225 - 9C + 8C}{2} = 106$

$225 - 9C + 8C = 2(106)$

$225 - C = 212$

$C = 225 - 212$

$C = \ 13$

Substitute the value of C into eq. 2

$A = \frac{75 - 3(13)}{2}$

$A = \frac{75 - 39}{2}$

$A = \ 18$

Therefore, the price of the​ adult's ticket is $18 and the price of a​ child's ticket is $13