system of equation word problem

Question

at the homecoming football game, the senior class officers sold slices of pizza for $.75 each and hamburgers for $1.35 each They sold 40 more slices of pizza than hamburgers and sales totaled $292.50 how many slices of pizza did they sell

Answer 1

HI Cori,

You can begin by writing two equations and two unknowns. Next, Identify your variables.

p = number of pizza slices, h = number of hamburgers

The first equation will show how much the pizza and burger cost

.75 x p + 1.35 x h = 292.50

The second equation will show a relationship between the number of pizza slices and hamburgers

p - h = 40

multiply the first equation by 100 to get rid of the decimals

75 x p + 135 x h = 29,250

rewrite the second equation solving for p.

p = h + 40

Substitute the value for p in the second equation into the first.

75 x (h+40) + 135 x h = 29,250

Solve the new equation for h

75h + 75 x 40 + 135h = 29,250

75h + 3000 + 135h = 29,250

210h + 3000 = 29,250

210h = 26,250

h=125

Since p = h + 40

p = 125 + 40, p = 165

So you have 125 hamburgers and 165 pizza slices

You can check your answer by multiplying 125 by 1.35 (cost per burger) and 165 by .85 (cost per slice) and

168.75 + 123.75 = 292.50 your original total.

I hope this helps and good luck!

Answer 2

Let x= hamburger and y=pizza. Then 1.35x +.75y = 292.5 and x+40=y so x=y-40 and using substitution the cost equation becomes 1.35(y-40) +.75y =292.5 so 1.35y +.75y -54 =292.5 2.1y = 346.5 and y=165.

Answer 3

h represents the number of hamburgers

h + 40 represents the number of pizza slices

1.35h + 0.75(h + 40) = 292.50

Can you solve for h and answer?