Question

Lesson Practice - Part 1 Choose the correct answer. 11 6 adulisand child c 10 adultikes and 4 cha Dadurackers and 2 chic

Answer 1

We want to solve the following system of equations

$x+y=14$

and

$4x+y=38$

where x is the number of adult tickets sold and y is the number of child tickets sold.

From the first equation, we can deduce that

$y=14-x$

If we replace this value on the second one, we get

$4\cdot x+(14\text{ -x)=38}$

If we operate on the left hand side, we get

$4x\text{ -x +14 = 3x+14=38}$

Then, if we subtract 14 on both sides, we get

$3x=38-14=24$

Finally, if we divide both sides by 3, we get

$x=\frac{24}{3}=8$

If we replace this value in the original equation, we have that

$y=14-8=6$

So 8 adult tickes and 7 child tickets were sold in total.