ABC gifts

Arthur had 30 dollars to spend on three gifts. He spent 9 3/4 dollars on gift A and 4 1/2 dollars on gift B. How much money did he have left for gift C?

Correct answer:

C =  15 ³⁄₄ = 63/4 USD

Step-by-step explanation:

$$\begin{gathered} G=30\text{USD} \\ A=9\frac{3}{4}=9+\frac{3}{4}=\frac{9\cdot 4+3}{4}=\frac{36+3}{4}=\frac{39}{4}=9.75\text{USD} \\ B=4\frac{1}{2}=4+\frac{1}{2}=\frac{4\cdot 2+1}{2}=\frac{8+1}{2}=\frac{9}{2}=4.5\text{USD} \\ A+B+C=G \\ S=A+B=\frac{39}{4}+\frac{9}{2}=\frac{39}{4}+\frac{18}{4}=\frac{39+18}{4}=\frac{57}{4}=14.25\text{USD} \\ C=G-S=30-\frac{57}{4}=\frac{30\cdot 4}{4}-\frac{57}{4}=\frac{120}{4}-\frac{57}{4}=\frac{120-57}{4}=\frac{63}{4}=\frac{63}{4}\text{USD}=15\frac{3}{4}\text{USD}=15.75\text{USD} \end{gathered}$$

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