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# 7 t-shirts and a hat costs £67.00 5 t-shirts and a hat costs £49.00. How much does a t-shirt cost? How much does a hat cost?

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7 t-shirts and a hat costs £67.00 5 t-shirts and a hat costs £49.00. How much does a t-shirt cost? How much does a hat cost?

Mar 27, 2020

### 1+0 Answers

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7 t-shirts and a hat costs £67.00

5 t-shirts and a hat costs £49.00.

How much does a t-shirt cost?

How much does a hat cost?

Let t-shirt $$= x$$
Let hat $$= y$$

$$\begin{array}{|lrcll|} \hline (1) & 7x+y &=& 67 \\ (2) & 5x+y &=& 49 \\ \hline (1)-(2): & 7x+y -(5x+y) &=& 67-49 \\ & 7x+y -5x -y &=& 18 \\ & 7x -5x &=& 18 \\ & 2x &=& 18 \quad | \quad :2 \\ & \mathbf{x} &=& \mathbf{9} \\ \hline & 5x+y &=& 49 \quad | \quad \mathbf{x=9} \\ & 5*9+y &=& 49 \\ & 45 + y &=& 49 \\ & y &=& 49-45 \\ & \mathbf{y} &=& \mathbf{4} \\ \hline \end{array}$$

A t-shirt does $$\mathbf{£9.00}$$ cost?
A hat does $$\mathbf{£4.00}$$ cost?

Mar 27, 2020