Question

if 10 shifts cost $120 and 30 shirts cost $310 write a linear equation that gives the cost C for n shirts

Answer 1

We will use a simultaneous approach since the rates are seemingly different.

We will create a relationship using the general line equation, y = mx + c.

Where:

y = Cost, C according to our question

m = line gradient

x = no of shirts, n

c = line intercept on y / cost axis, we will call this b since we already have C

Thus, we will have:

$C=mn+b\ldots0$

So, inputting variables from our question, we have:

$\begin{gathered} 120=10m+b\ldots1 \\ 310=30m+b\ldots2 \\ Eliminating\text{ b, we subtract eqn 1 from 2 to get:} \\ 190=20m \\ We\text{ divide both sides by 20 to get our m to be:} \\ \frac{190}{20}=\frac{20m}{20} \\ m=9.5 \end{gathered}$

We now substitute this value of m into the equation 1 to get:

$\begin{gathered} 120=10(9.5)+b=95+b \\ \text{subtract }95\text{ from both sides to get:} \\ 120-95=b \\ b=25 \end{gathered}$

Finally, we substitute the values of m and b into equation 0 to get:

C = 9.5n + 25