# SAT Math Multiple Choice Question 800: Answer and Explanation

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**Question: 800**

**5.** The total fare for two adults and three children on an excursion boat is $14. If eachchild's fare is one-half of each adult's fare, what is the total cost for one adultand one child?

- A. $4.00
- B. $5.25
- C. $6.00
- D. $6.50

**Correct Answer:** C

**Explanation:**

**C**

**Difficulty:** Medium

**Category:** Heart of Algebra / Systems of Linear Equations

**Strategic Advice:** Use the Kaplan Strategy for Translating English into Math to write two equations that represent the scenario. Use variables that make sense to help you stay organized (such as *a* for adult and *c* for child).

**Getting to the Answer:** Use the information given to write two equations in words first:

Two adult fares plus 3 child fares equals 14 → 2*a* + 3*c* = 14

One child fare equals one-half an adult fare →

If you don't like working with fractions, multiply both sides of the second equation by 2 to get 2*c* = *a*. Then, plug 2*c* in for *a* into the first equation and solve for *c*:

The cost of a child's fare is $2, which is half the cost of an adult's fare. This means an adult's fare costs $4. Don't fall for the trap answer, which is A. Add the two fares together to find that the total cost for one adult and one child is $6, which is (C).