# equationsWhat are the equations for these paterns? 1 lap              \$1               \$2 2 laps             \$3               \$3.50 3...

equations

What are the equations for these paterns?

1 lap              \$1               \$2

2 laps             \$3               \$3.50

3 laps             \$5               \$5

4 laps             \$7               \$6.50

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We see that the numbers corresponding to 1 lap are \$1 and \$2, for an increase in the number of laps by 1, the first number increases by 2 and the next by 1.5. Let the number of laps be x which is the independent variable, and the number in the 2nd and 3rd columns be represented by y1 and y2.

We get the equations:

y1 = 1 + 2(x - 1) and y2 = 2 + 1.5(x - 1).

neela | High School Teacher | (Level 3) Valedictorian

Posted on

We set up the following linear equations, in accordance with the quantities and try determine x,y .

x+y=2

2x+3y=3.5

3x+5y=5

4x+7y=6.5

From (1) and (4)  eliminating x we get,

(4)-3*(1):  3y=6.5-8=-1.5. Therefore, y= -1.5/3= -0.5. Re substituting this value of y in(1), x-0.5 =2=>x =2.5.

We see that  the value of x and y fits well to all the patterns.