Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.7 National olympiad Find the answer

Jerry and Hannah Kubik live in Jupiter Falls with their five children. Jerry works as a Renewable Energy Engineer for the Southern Company, and Hannah runs a lab at Jupiter Falls University where she researches biomass (renewable fuel) conversion rates. Michael is their oldest child, and Wendy their oldest daughter. Tony is the youngest child. Twins Joshua and Alexis are $12$ years old.

When the Kubiks went on vacation to San Diego last year, they spent a day at the San Diego Zoo. Single day passes cost $\$ 33 $for adults (Jerry and Hannah),$ \ $22$ for children (Michael is still young enough to get the children's rate), and family memberships (which allow the whole family in at once) cost $\$ 120$. How many dollars did the family save by buying a family pass over buying single day passes for every member of the family?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

1. Identify the cost of single day passes for adults and children:
- Adult pass: \$33
- Child pass: \$22

2. Determine the number of adults and children in the family:
- Adults: 2 (Jerry and Hannah)
- Children: 5 (Michael, Wendy, Tony, Joshua, and Alexis)

3. Calculate the total cost of single day passes for the entire family:
- Cost for adults: $2 \times 33 = 66$ dollars
- Cost for children: $5 \times 22 = 110$ dollars
- Total cost using single day passes: $66 + 110 = 176$ dollars

4. Compare the total cost of single day passes with the cost of a family membership:
- Family membership cost: \$120

5. Calculate the savings by buying a family membership instead of single day passes:
- Savings: $176 - 120 = 56$ dollars

Conclusion:
The family saved $\boxed{56}$ dollars by buying a family pass over buying single day passes for every member of the family.

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