Chapter 1.5, Problem 4GP

To determine

How much is her allowance.

Answer to Problem 4GP

  $\$8$

Explanation of Solution

Given :

Tia used half of her allowance to buy a ticket to the class play. Then she spent $1.75 for ice cream. Now she has $2.25 left.

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

In order to find how much is her allowance, first let the total allowance be x then she used half of her allowance to buy a ticket to the class play, that is x /2, then she spent $1.75 for ice cream and she has $2.25 left, adding three of them equal to total allowance, that is x so, the expression is as shown below:

  $\frac{x}{2}+\$1.75+\$2.25=x$

Now to solve the above equation, first adding the term in left side which don’t have any variable, then subtract x/2 from both sides and then multiply both sides by 2 as shown below:

  $\begin{array}{l}\frac{x}{2}+\$1.75+\$2.25=x\\ \frac{x}{2}+\$4=x\\ \frac{x}{2}-\frac{x}{2}+4=x-\frac{x}{2}\\ 4=\frac{x}{2}\\ 4\times 2=\frac{x}{2}\times 2\\ 8=x\end{array}$

So, her allowance is $8