There are 8 tickets for a family to go to a concert. adult tickets are $15 each and children’s tickets cost $10 each. the family spent $105. how many of each ticket did they buy?

Let...

a=number of adult tickets

c=number of children tickets

Equations:

a+c=8

15a+10c=105

Solve by substitution.

a+c=8 > a=8-c

15a+10c=105

15(8-c)+10c=105

120-15c+10c=105

120-5c=105

-5c=-15

c=3

a+3=8

a=5

3 children tickets and 5 adult tickets

A) no solution

Step-by-step explanation:

The given system of equations are:

4x - 5y = 5

-0.08x + 0.10y  = 0.10

Let's find the slope of the each equation.

4x - 5y = 5

Write the equation in slope-intercept form y = mx + b.

-5y = -4x + 5

Dividing both sides by -5, we get

y = -4/-5 x +5/-5

y = 0.8x - 1

Here slope = 0.8 and y-intercept (b) = -1

-0.08x + 0.10y = 0.10

0.10y = 0.08x + 0.10

Divide both side by 0.10, we get

y = 0.8x + 1

Here the slope = 0.8 and y-intercept (b) = 1

From the both the equations, the slopes are the same and y-intercepts are different.

Therefore, the given system of equations are parallel.

If the system of equations are parallel, then there is no solution.