Answer:
System is as below:
5x + 2y = 45 (equation 1)
2x + 5y = 39 (equation 2)
Solving the system results in:
x =7
y = 5
Step-by-step explanation:
Given data:
One family paid $45 for 5 adults and 2 children.
The other family paid $39 for 2 adults and 5 children.
<em>Let the price for an adult be x</em>
<em>Let the price for a child be y</em>
The system of equation will be
5x + 2y = 45 <em>(equation 1)</em>
2x + 5y = 39 <em> (equation 2)</em>
<em>Solving the equation using elimination method</em>
<em>Eliminate x by the coefficients of x in equation 1 and 2</em>
5x + 2y = 45 <em>(Multiply the whole equation by 2)</em>
2x + 5y = 39 <em>(Multiply the whole equation by 5)</em>
10x + 4y = 90
10x + 25y = 195 <em>(Subtract the equation)</em>
0x + (-21y) = (-105)
-21y = -105
y= 5
<em>Substituting y into equation 1</em>
5x + 2y = 45
5x + 2(5) = 45
5x +10 = 45
5x = 45-10
5x = 35
x =7