670 tickets were sold. adult tickets are $8 and child tickets are $5. the total sales was $4190. how many of each tickets were sold?

child tickets sold= x

adult tickets sold = y

equation 1

x + y = 670

solve for y

x + y = 670

subtract x from both sides

y= 670- x

equation 2

5x + 8y =4190

plug in equation 1 into equation 2

5x + 8 (670- x)=4190

distribute:

5x + 5,360- 8x=4190

solve for x

step 1 combine like terms

5x- 8x = -3x

-3x+5,360=4190

subtract 5,360 from both sides

-3x= -1,170

divide by -3

x=390

you know x now plug it in

5 (390) + 8y=4190

1,950+8y=4190

-1950. -1950

8y=2,240

divide both sides by 8

y=280

back to original equation 1

y+x=670

plug y and x in

280+390= 670

in conclusion 280 adult tickets were sold and 390 child tickets were sold.

this was killing me

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.