SYSTEMS OF EQUATIONS

I have bought three pens and a marker for €6. My friend Rosa has paid €9.25 for two pens and three markers. How much does one pen cost? What about a marker?

• x+y=6

• 3x+y=6

• 2x+3y=9,25

• x+2y=9,25

Calculate two numbers knowing that the difference between them is 16, and that double the smaller number is five more than the bigger number.

• x-y=16

• 2x=y+5

• 2y=x+5

• 2y+x=5

A customer has paid €3.90 for one kilo of oranges and two kilos of apples at the greengrocer. Another customer has paid €5.70 for three kilos of oranges and one kilo of apples. How much does one kilo of oranges cost? What about one kilo of apples?

• x+y=3,90

• 3x+y=3,90

• x+2y=3,90

• 3x+y=5,70

Last week we paid €10 for two tickets to the movies and a box of popcorn. Today we paid €22 for four tickets and 3 boxes of popcorn. How much does one ticket cost? And how much does one box of popcorn cost?

• 4x+3y=22

• 2x+y=22

• 2x+y=10

• 4x+3y=10

Coffee A is of higher quality and costs €13/kg. Coffee B is of lower quality and costs €8/kg. How much of each do we need to get 30 kilos of coffee mixture that costs €10/kg?

• x+y=30

• 13x+8y=30

• 13x+8y=30·10

• x+y=10

What quantities of gold, at €8/gram and silver at €1.70/gram do we need to make 1 kg of an alloy that costs €4.22/gram?

• x+y=1000

• 8x+1,70y=1000 · 4.22

• 8x+1,70y= 1000

• x+y=4.22

On a farm, there are 12 heads and 34 legs between pigs and chickens. How many pigs are there? How many chickens are there?

• 4x+2y=34

• 4x+2y=12

• x+y=12

• x+y=34

Rosendo has 12 coins in his pocket: some are 20-cent coins and some are 50-cent coins. If he has a total of €3.30, how many coins of each type does he have?

• x+y=20

• 20x+50y=3,30

• 0,20x+0,50y=3,30

• x+y=12

For the purchase of two appliances we have paid €3,500. If they had given us a 10% discount in the first one and an 8% discount in the second one, we would have paid 3100€. What is the price of each item?

• x+y=3500

• 0,10x+0,08y=400

• 0,10x+0,08y=3100

• 10x+8y=400

In a multiple choice test, 4 is scored for each correct answer and one point is subtracted for a wrong one. A student answers 17 questions and obtains 43 points. How many questions did you answer correctly?

• x+y=17

• 4x+y=43

• 4x-y=43

• x+y=43