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**Question 12:**

Keluarga Pak Azril ingin mengadakan Hari Keluarga. Mereka bercadang untuk menempah \( x \) helai kemeja-T dewasa dan \( y \) helai kemeja-T kanak-kanak untuk hari itu. Jumlah tempahan kedua-dua jenis kemeja-T itu adalah tidak lebih daripada 70 helai dan jumlah bilangan tempahan kemeja-T kanak-kanak adalah sekurang-kurangnya dua kali bilangan kemeja-T dewasa.

**Translation:**

Pak Azril's family wants to organize a Family Day. They plan to order \( x \) t-shirts for adults and \( y \) t-shirts for children for the day. The total number of both types of t-shirts is no more than 70 and the number of t-shirts for children is at least twice the number of t-shirts for adults.

**Given conditions:**

1. \( x + y \leq 70 \)
2. \( y \geq 2x \)
3. \( x \geq 0 \)
4. \( y \geq 0 \)

**(a) Write two linear inequalities, other than \( x \geq 0 \) and \( y \geq 0 \), which represent the situation.**

The inequalities are:
1. \( x + y \leq 70 \)
2. \( y \geq 2x \)

**(b) For this part of the question, use the graph paper provided on page KM 2 (K2) - 9. Using a scale of 2 cm to 10 t-shirts on both axes, \( x \) and \( y \), draw and shade the region that satisfies the system of linear inequalities in 12(a).**

Refer to the graph paper and plot the lines \( x + y = 70 \) and \( y = 2x \). Shade the feasible region.

**(c) From the graph drawn,**

**(i) determine the maximum number of t-shirts for children if the number of t-shirts for adults purchased is 20.**

Substitute \( x = 20 \) into the inequality \( x + y \leq 70 \):
\[ 20 + y \leq 70 \]
\[ y \leq 50 \]

Substitute \( x = 20 \) into the inequality \( y \geq 2x \):
\[ y \geq 2(20) \]
\[ y \geq 40 \]

Therefore, the maximum number of t-shirts for children, \( y \), when \( x = 20 \) is:
\[ 40 \leq y \leq 50 \]

**(ii) Based on the answer in 12(c)(i), calculate the total amount of money that Pak Azril's family needs to pay if the price of a t-shirt for adults is RM35 and a t-shirt for children is RM20.**

If \( x = 20 \) and \( y \) is between 40 and 50, let's assume \( y = 50 \) for maximum amount calculation:

Total cost = \( (20 \times 35) + (50 \times 20) \)
\[ = 700 + 1000 \]
\[ = 1700 \]

So, the total amount of money Pak Azril's family needs to pay is RM1700.

Do you want further details or have any questions? Here are some related questions to expand the topic:

1. How would the solution change if the prices of the t-shirts were different?
2. What is the

Keluarga Pak Azril ingin mengadakan Hari Keluarga. Mereka bercadang untuk menempah x helai kemeja-T dewasa dan y helai kemeja-T kanak-kanak untuk hari itu. Jumlah tempahan kedua-dua jenis kemeja-T itu adalah tidak lebih daripada 70 helai dan jumlah bilangan tempahan kemeja-T kanak-kanak adalah sekurang-kurangnya dua kali bilangan kemeja-T dewasa.

Solve a family t-shirt order problem involving linear inequalities. Learn how to determine the maximum number of t-shirts for children given adult t-shirt quantities, graphing constraints, and calculating costs. Suitable for Grades 10-12.

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