Question

4. Check and solve the three possible combinations
5. Graph the inequality and plot the three possible combinations in the plane.​

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Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

Number of Graham balls she purchased be x

Number of Yema Candies she purchased be y

Now, Given that

Cost of 1 Graham ball is php 5

Cost of 1 Yema candy is php 4

So,

Cost of x Graham ball is php 5x

Cost of y Yema candy is php 4y

Now, she has only php 50 to purchase these.

$\rm\implies \:5x + 4y \leqslant 50$

Note :-

$\rm \: x \geqslant 0 \: \: and \: \: y \geqslant 0$

To plot this, let we find the points on the line

$\rm \: 5x + 4y = 50$

Substituting 'y = 0' in the given equation, we get

$\rm \: 5x + 4(0) = 50$

$\rm \: 5x + 0 = 50$

$\rm \: 5x = 50$

$\rm\implies \:x = 10$

Substituting 'y = 5' in the given equation, we get

$\rm \: 5x + 4(5) = 50$

$\rm \: 5x +20 = 50$

$\rm \: 5x = 50 - 20$

$\rm \: 5x = 30$

$\rm\implies \:x = 6$

Substituting 'y = 10' in the given equation, we get

$\rm \: 5x + 4(10) = 50$

$\rm \: 5x + 40 = 50$

$\rm \: 5x = 50 - 40$

$\rm \: 5x = 10$

$\rm\implies \:x = 2$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 10 & \sf 0 \\ \\ \sf 6 & \sf 5 \\ \\ \sf 2 & \sf 10 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (10 , 0), (6 , 5) & (2 , 10)

➢ See the attachment graph.