Write System of Equations from Context

Question

Annabelle is going to a carnival that has games and rides. Each game costs $1.75 and each ride costs $3.50. Annabelle spent $28 altogether at the carnival and the number of games she played is 7 more than the number of rides she went on. Graphically solve a system of equations in order to determine the number of games Annabelle played, x, and the number of rides Annabelle went on, y.

I need...

Let_=________________________

Let_=________________________

System of Equations

__________________

__________________

Answer 1

"Each game costs $1.75 and each ride costs $3.50. Annabelle spent $28 altogether at the carnival"

Let 28 = 1.75G + 3.5R

"the number of games she played is 7 more than the number of rides she went on"

Let G = R + 7

determine the number of games Annabelle played, x, and the number of rides Annabelle went on, y.

28 = 1.75x + 3.5y

x = y + 7

Graphically solve

draw the equations, find the intersection

rearrange equation in slope intercept form (easier to plot)

28 = 1.75x + 3.5y

=> 3.5y = -1.75x + 28

=> 7y = -3.5x + 56

=> y = - 1/2 x + 8 with slope = -1/2 and y intercept = 8

hence draw line passing through (0,8) and (2, 7)

x = y + 7

=> y = x - 7 with slope = 1 and y intercept = -7

hence draw line passing through (0,-7) and (1, -6)

intersection from graph at (10,3) = 10 games and 3 rides

double check?

10 = 3 + 7 = 10

28 = 1.75(10) + 3.5(3) = 17.5 + 10.5 = 28

Answer 2

Hi Bob A

Games cost 1.75

Rides cost 3.50

Total funds spent = 28.00

Rides = y

Games = x = y + 7

And x - y = 7

And y = x - 7 In Slope Intercept Form

Your Equations are

Equation 1 for total cost

1.75x + 3.50y = 28.00

y = -1/2x + 8 In Slope Intercept Form

Equation 2 for number of games based on the relationship of x to y, where x = y + 7

x - y = 7

You can graph both equations at Desmos.com in Slope Intercept Form to find their common point

Or

You can easily eliminate y by multiplying Equation 2 by 3.5 then combining your equations

3.50x - 3.50y = 24.50

1.75x + 3.50y = 28.00

This yields

5.25x = 52.50

Divide both sides by 5.25 to solve for x

x = 52.50/5.25

x = 10

Substitute 10 for x in the original Equation 2

x - y = 7

10 - y = 7

Subtract from both sides of the equation

-y = -3

Divide both sides by -1 to solve for y

y = 3

I hope this helps

The problem can also be solved by substitution, since we are given x = y + 7

Substitute y + 7 in the Equation 1

1.75(y + 7) + 3.50y = 28.00