Question

(i) Devi notices that the cost per T-shirt decreases when more T-shirts are ordered and is puzzled
by the observation from the graph that 'O T-shirt costs $50'. Provide a possible explanation
(і) Со
C
this problem
(ii) Find the amount of money Devi has to pay for 68 T-shirts.
(iv) If Devi has a budget of $410, state the number of T-shirts she can order.​

Answer 1

SOLUTION

GIVEN

(i) The table from this problem

(ii) Find the amount of money Devi has to pay for 68 T-shirts.

(iii) Devi notices that the cost per T-shirt decreases when more T-shirts are ordered and is puzzled

by the observation from the graph that 'O T-shirt costs $50'. Provide a possible explanation

(iv) If Devi has a budget of $410, state the number of T-shirts she can order.

EVALUATION

(i) Here in the graph we see that along x axis ( horizontal axis) we take number of T shirts ( N ) & along y axis ( vertical axis ) there is the cost ( C )

We have

When N = 10 we have C = 100

When N = 30 we have C = 200

When N = 50 we have C = 300

When N = 70 we have C = 400

The table is as below

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c|c|c} \sf N &\sf 10&\sf \: 30&\sf \:50&\sf \: 70\\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}&\frac{\qquad}{}\\\\ \sf C & \sf 100&\sf 200&\sf300&\sf 400 \\\frac{\qquad}{}&\frac{\qquad}{}&\frac{\qquad \qquad}{}\\\sf & \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}$

(ii) We see from the graph that there is a linear equation to represent the situation

Two points on the line are (10,100) & ( 30,200)

Thus the equation is

$\displaystyle \sf{ \frac{N - 10}{C - 100} = \frac{30 - 10}{200 - 100} }$

$\displaystyle \sf{ \implies \: \frac{N - 10}{C - 100} = \frac{20}{ 100} }$

$\displaystyle \sf{ \implies \: \frac{N - 10}{C - 100} = \frac{1}{5} }$

$\displaystyle \sf{ \implies \: C - 100 = 5N - 50 }$

$\displaystyle \sf{ \implies \: C = 5N + 50 }$

Now we have to find the amount of money Devi has to pay for 68 T-shirts.

Here N = 68

So the required amount

= $ ( 5 × 68 ) + 50

= $ 340 + 50

= $ 390

The amount of money Devi has to pay for 68 T-shirts = $ 390

(iii) Now Devi notices that the cost per T-shirt decreases when more T-shirts are ordered and is puzzled by the observation from the graph that 'O T-shirt costs $50'

So there is a fixed overhead of $ 50

(iv) Now Devi has a budget of $410

We have to find the number of T-shirts she can order

So C = 410

$\displaystyle \sf{ 410 = 5N + 50 }$

$\displaystyle \sf{ \implies \: 5N = 360 }$

$\displaystyle \sf{ \implies \: N = 72 }$

Hence the number of T-shirts Devi can order = 72

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