Need Help - Using Stimultaneous Equations to solve word problems

[chuckjefster90]

Hey Guys, Would you be able to help me with these questions without using a calculator?
Im struggling on how to solve them. I've put the answers at the bottom.
Thanks Heaps.

1. In a particular week, a 'budget' manufacturer sells a total of 15 tables and chairs and recieves $480. If a table sells for $60 and a chair for $25, how many of each are sold?

2. At a primary school tuck shop three salad rolls and four pies cost $10.28. A salad roll is 58c dearer than a pie. How much does each cost?

3. The sum of two numbers is 38 and their difference is 24. What are the numbers?

4. In Ellen's piggy bank there are 18 coins totalling $1.65. If she has only 5 cent and 10 cent coins, how many of each does she have?

5. A factory that produces wooden toys has equipment costs of $3500 and then a cost of $35 per toy made. Each toy is then sold for $55.
a) Write a rule for the costs, C when x toys are made

b) Write a rule for the revenue, T, when x toys are sold

c) Determine the 'break even' point.

d) How many toys need to be sold for the factory to make a profit?

Answers
1) 3 tables, 12 chairs      2) Pies -$1.22, Salad Roll - $1.80          3) 7, 31      4) 3 5cent coins, 15 10cent coins         
5a) C  = 3500 +35x      b) R = 55x        c) 175 toys           d) >175

[superflya]

most, if not all these questions can be done by constructing simultaneous equations.

[m@tty]

Firstly for these type of questions you need to form the equations, which can generally be easily deduced from the given statement. The first question says that . Here let number of chairs = c and number of tables = t.The question also states, keeping in mind that the price of a chair is $25 and a table is $60, that .
Form there you can solve the two equations simultaneously:
Equation 1:

(equation 3)
Equation 2:


Sub equation 3 into equation 2:









Therefore , as

So there were 12 chairs and 3 tables.

[the.watchman]

Yep, and don't be afraid to introduce variables to help you, like what m@tty has done in his working.
Look for any information in the question and apply the variables to this.

[chuckjefster90]

ahokay ill give it a go
thankss

[luken93]

I mightaswell contribute

2)At a primary school tuck shop three salad rolls and four pies cost $10.28. A salad roll is 58c dearer than a pie. How much does each cost?
Let roll be r and pie be p
(1)
(2)

Sub (2) into (1)





Pie = $1.22

Sub Pie into (2)



Roll is $1.80
Pie is $1.22

And to check

[the.watchman]

3) Let the two numbers be x and y

So (1)     AND (2)

(1) + (2): ,   

So ,   



4) Let the number of five cent coins be x and the number of ten cent coins be y

So ,    (1)

And (2)

(2) - (1): ,   

So



5) (a)


(b)


(c) Let

So ,    ,   


(d) For , it is obvious that

[chuckjefster90]

THANK YOU SO MUCH