# Grid-Ins

## Student-Produced Response

The sum of *r* and *p* is equal to twice *s*, and *p* is 36 less than twice the sum of *r* and *s*. What is the value of *r* ?

Correct Answer: 12

**Explanation:**

The phrase "the sum of *r* and *p* is equal to twice *s*" can be written as *r* + *p* = 2*s*. The phrase "*p* is 36 less than twice the sum of *r* and *s*" can be written as *p* = 2(*r* + *s*) - 36. From the first equation, *p* = 2*s* - *r*. Substituting this expression for *p* into the second equation yields

2s - r | = | 2(r + s) - 36 |

2s - r |
= | 2r + 2s - 36 |

-r |
= | 2r - 36 |

-3r |
= | -36 |

r |
= | 12 |

The value of *r* is 12.

(from the October 12, 1999 test)