Question

Hannah got a perfect score on 3 more spelling quizzes this quarter than last quarter. If she doubles the number of perfect quizzes she had this quarter, she will tie the school record. The record is 3 times the number of spelling quizzes hannah scored perfectly on last quarter.
A) Write an expression for the # of perfect spelling quizzes Hannah had this quarter. What does the variable represent?
B) Write an expression for the record number of perfect spelling quizzes.
C) Use the expressions from A & B to solve an equation to find the # of perfect spelling quizzes Hannah had last quart

Answer 1

The key to solving such questions is to develop a relationship between the information you are provided with. By looking at the first statement you can see that the score of the current quarter is dependent on the score of the last quarter.
Therefore:
\[\text{Let the score of last quarter =}\quad x\\\] Her current score is 3 more than her last one so
\[\text{Current Score =}\quad x+3\]

Answer 2

For the second part of the question you are provided with information about the school record in two different ways.
Firstly, you are told what the school record is in comparison to the current quarter score of Hannah. Secondly, you are told what the school record is compared with the last quarter score of Hannah.

This can be expressed mathematically as
\[\text{The school record is double of Hannah's current score:}\quad 2(x+3)\]
\[\text{The school record is three times Hannah's last score:}\quad 3(x)\]

Answer 3

I hope you'll be able to solve the last part by yourself now.