Algebra Solution

Question

(1) Solve this system using the substitution method: y = x + 3; y – x = 8

(2) Solve this application problem using a system of equations: Solve this application problem using a system of equations: Ron and Wanda are ticket sellers for their class play. Ron sells student tickets for $2.00 each, and Kathy sells adult tickets for $4.50 each. If their total revenue for 369 tickets is $1175.50, then how many tickets did Ron sell?

Answer 1

1. y = x + 3----> y = x + 3

y - x = 8----> y = x + 8

both are rearranged into y intercept form and we see they are not equal so no solution

R + W = 369 re wrote

R(2) + W (4.5) = 1175.50------> R(2) = -W(4.5) + 1175.50 = R = -W2.25 + 587.75

2

substitute R = - W2.25 + 587.75

-W2.25 + 587.75 + W = 369----> -W1.25 = -587.75 + 369----> -W1.25= -218.75 W = 175

If W = 175 then R = 194 because 369 - 175 is 194

Answer 2

y - x = 8

x+3 - x = 8 <-- substitution

3 = 8

no solution

By elimination just to verify:

y-x = 3 is the first equation and y-x = 8 is the given second equation

y-x cannot be equal to two different values. Elimination gives 0 = 5,

so no solution

Now for the work problem:

A+s = 369

2s + 4.5 A = 1175.50

2s + 4.5 (369 - s) = 1175.50

2s + 1660.5 - 4.5s = 1175.50

-2.5s + 1660.5 = 1175.50

-2.5s = -485

s=194

then a = 369-194 = 175

4.5 * 175 + 2 * 194 = 787.5 + 388 = 1175.50

194 student tix

175 adult tix