PROBLEMS : SYSTEMS of EQUATIONS in TWO VARIABLES (x ,y)

1.- The addition of two numbers is 100 and the difference between them is 80.

Try to find both numbers

2.- And find two other numbers whose addition is 93 and their difference is 21.

3.- One kilogram of apples is 0,5 Euros more expensive than one kilo of bananas.

If you pay 3,5 Euros for one kilo of apples and one of bananas,

how much money will one kilo of each fruit cost?

4.- The ticket of the swiming pool is 2 Euros cheaper than the ticket of the cinema.

If you have 10 Euros and you go to the pool in the morning and to see a movie in the afternoon, but after that, you still have 4 Euros left, how much does it cost each ticket?

5.- Imagine that you pay 50 Euros for a jeans and a green shirt. You don't remember how much does it cost every thing, but you know that the pants were 8 Euros more expensive than the shirt.

Try to find the price of both separately.

6.- In a restaurant, you can find two type of sandwitches, one of cheese for 2 Euros each, and

another of ham for 3,5 Euros each one.

Last week, 52 sandwitches were sold and the total amount of cash was 149 Euros.

Try to calculate the number of each sandwith that was sold.

7.- Yesterday I went on sales, and I paid only 90,50 Euros for a white shirt and a sweater which

cost 110 Euros before sales.

The price of the shirt was reduced 20 % and the sweater's price had a discount of 15 % .

What was the original prices of each article going on sales?

8.- A stock market investor put part of his capital of 28000 $ in a bank B1 with an interest rate of

8 %, and separately, he puts the rest of the money in another bank B2 at an interest rate of 6 %.

For the first part of the money, the investor will get 200 $ more benefits than for the second part, how much money has he invest in each bank ?

9.- The salary of a salesman who works on a commission- only basis, is equal to a fixed steady part plus some percentatge( called commision ) that depens on the sales he can do every month.

If this salesman sells 2000 Euros, his salary would be 1200 Euros, but if he sells 2500 Euros then his salary would rise to 1300 Euros.

How much would he have to sell to get a salary of 1500 Euros?

Try to find the percentatge he earns depending on the sales he does.

10.- The ticket's price of an intercity bus line, depens on the kilometers.

So, you pay 18 Euros to go to a city 500 Km far from here but you pay 33 Euros for another city 1000 Km away.

How much would you pay if you wanna go 750 Km from here?

Hi people! soon you will have the answers...

by JL