Question

four families go to the cinema. the reid family take 2 adults and 2 children for £18 ; the mghee family take 1 senior, 2 adults and 1 child for £18.50; and the griffiths family take 1 senior and 3 adults for £19.50. how much will it cost the Linton family to take 1 senior, 2 adults and 3 children?

Answer 1

Answer:

$\pounds 26.50$

Step-by-step explanation:

Let

x = cost for one adult

y = cost for one child

z = cost for one senior.

The Reid family:

take 2 adults and 2 children and paid $2x+2y$ that is $\pounds 18$, so

$2x+2y=18$

The Mghee family:

take 1 senior, 2 adults and 1 child and paid $x+2x+y$ that is $\pounds 18.50$, so

$x+2x+y=18.50$

The Griffiths family:

take 1 senior and 3 adults and paid $z+3x$ that is $\pounds 19.50$, so

$z+3x=19.50$

You get the system of three equations:

$\left\{\begin{array}{l}2x+2y=18\\ \\z+2x+y=18.50\\ \\z+3x=19.50\end{array}\right.$

From the first equation:

$2y=18-2x\\ \\y=9-x$

From the third equation:

$z=19.50-3x$

Substitute them into the second equation:

$19.50-3x+2x+9-x=18.50\\ \\-3x+2x-x=18.50-19.50-9\\ \\-2x=-10\\ \\2x=10\\ \\x=5$

Then

$y=9-5=4\\ \\z=19.50-3\cdot 5=19.50-15=4.50$

Hence,

the cost for one adult is $\pounds 5$

the cost for one child is $\pounds 4$

the cost for one senior is $\pounds 4.50$

The Linton family takes 1 senior, 2 adults and 3 children and paid

$\pounds 4.50+2\cdot \pounds 5+3\cdot \pounds 4=\pounds 26.50$