My name is Laura Molck and I am in Year 11 in Australia. Please help me with the following.I know that they are all simultaneous equations which I can do but I have trouble with the formulae to work the equations. Can you please help!!!!

Thank you

Laura Molck

1. A tent manufacturer produces 2 models, Outback and Bushwalker. From earlier sales records it is known that 20% more of the Outback model is sold than the Bushwalker. A profit of $200 is made on each Outback sold, but $350 is made on each Bushwalker. If during the next year a profit of $177,000 is planned how many of each model must be sold?

(Answer 360 Outbacks and 300 Bushwalkers.)

2. Oz Jeans has factories in two cities, Mydney and Selbourne. At the Mydney factory fixed costs are $28,000 per month and the cost of producing each pair of jeans is $30. At the Selbourne factory fixed costs are $35,200 per month and each pair of jeans costs $24 to produce. During the next month OzJeans must manufacture 6,000 pairs of jeans. Calculate the production order for each factory if the total manufacturing costs for each factory are to be the same.

(Answer is Mydney $2,800 and Selbourne $3,200.)

3. A tea wholesaler blends together 3 types of tea that normally sell for $10, $11 and $12 per kilogram so as to obtain 100 kg of tea worth $11.20 per kilo. If the same amounts of the two higher priced teas are used calculate how much of each type must be used in the blend.

(Answer 20 kg @ $10, 40 kg @$11 and 40 kg @$12).

Hi Laura,

I'll help with the first problem and hopefully that will get you started.

You are told that the profit planned for next year is $177,000 and you know how much profit each model gives, so that should give you one equation. Let x be the number of Outbacks sold and y the number of Bushwalkers sold then the profit from the Outbacks is $200 times x and the profit from the Bushwackers is $350 times y. The total profit, $177,00 is the sum, so

200 x + 350 y = 177,000

You also know that 20% more of the Outback model is sold than the Bushwalker, that is the number of Outbacks sold is 1.20 times the number of Bushwakers sold. Thus

x = 1.20 y

Now you have two equations to solve for x and y.

Cheers,
Penny
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