Solving word problems with a table

Last updated: 18 Nov 2008

We reduced the question to the following table.

% tickets sold price % total income
club members 50% \$11
children 10% \$5
non-members   \$15 ?

We will add a totals row because we are working with percentages and an income column so that we can later work out the percentages for the income.

We can fill in 100% for the totals of the percentages.

% tickets sold price % total income income
club members 50% \$11
children 10% \$5
non-members   \$15 ?
total 100% - 100%

Then it is a matter of filling in as many cells as we can calculate until we have enough information to find the answer.

In this case we know the % tickets sold will sum to 100% so the percentage sold to club members will be

$\lineskip 1em \begin{split} \%\text{non-members} &= 100\% - (\%\text{club members} + \%\text{children}) \\ &= 100\% - (50\% + 10\%) \\ &= 40\% \end{split}$
% tickets sold price % total income income
club members 50% \$11
children 10% \$5
non-members 40% \$15 ?
total 100% - 100%

Now we will work out the amount of income from each group.

The income from each group will be the number of tickets sold multiplied by the price of each ticket.

Since we do not know the total number of tickets sold we can assume that there were 100 tickets because this will make the mathematics easier.

$\lineskip 1em \begin{split} \text{income} &= \text{number of tickets sold} \times \text{price of ticket} \\ \text{income from club members} &= 50 \times \11 = 550 \\ \text{income from children} &= 10 \times \5 = \50 \\ \text{income from non-members} &= 40 \times \15 = \600 \\ \text{total income} &= \550 + \50 + \600 = \1200 \end{split}$
% tickets sold price % total income income
club members 50% \$11   \$550
children 10% \$5   \$50
non-members 40% \$15 ? \$600
total 100% - 100% \$1,200

Now that we have the total income and the income from non-members we can find the percentage we need.

$\lineskip 1em \begin{split} \frac{\text{non-members}}{\text{total}} &= \frac{600}{1200} \\ &= \frac{1}{2} \\ &= 50\% \end{split}$
% tickets sold price % total income income
club members 50% \$11   \$550
children 10% \$5   \$50
non-members 40% \$15 ? = 50% \$600
total 100% - 100% \$1,200

Returning to the question.

At a football game 50% of the seats are sold to season ticket holders who pay \$11 each and 10% are sold to children who pay \$5 each. All the remaining tickets are sold to non-members at \$15 each. What proportion of the total gate receipts for the game is contributed by non-members?

1. 60%
2. 52%
3. 50%
4. 40%
5. 5%

50% was contributed by non-members so the answer is C.

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