Bob bought popcorn, a soda, and a hotdog for $8.77. Popcorn costs $2 more than a hotdog. A soda costs $0.73 less than a hotdog. How much is each item?

Question

Bob bought popcorn, a soda, and a hotdog for $8.77. Popcorn costs $2 more than a hotdog. A soda costs $0.73 less than a hotdog. How much is each item?

Answer 1

p = h + 2 (popcorn equation)

s = h - 0.73 (soda equation)

p + s + h = 8.77 (equation for total purchase)

(h+2) + (h - 0.73) + h = 8.77 (substituting values for popcorn and soda in term of hot dogs)

3h + 1.27 = 8.77

3h = 7.5 (subtract 1.27 on both sides)

h = 2.5 (price of hot dog)

Substitute h=2.5 in each initial equation to solve for the rest if the items

p = (2.5) + 2 = 4.5 (price of popcorn)

s= (2.5) - 0.73 = 1.77 (price of soda)

Answer 2

P=200+H

P+S+H = 877

S=H-73

200+H + H-73 + H = 877

3H = 877+73 -200 = 750

H= 750/3 = $2.50 for a hot dog

S= 250-73 = $1.77 for a soda

P = 250+200= $4.50 for popcorn

Answer 3

Let the Popcorn be: P

Let the Soda be: S

Let the Hotdog be: H

Popcorn cost 2 more than the Hotdog, so:

P = H + 2

Soda cost 0.73 less than the Hotdog, so:

S = H - 0.73

All Popcorn, Soda and Hotdog together cost $8.77, so:

P + S + H = 8.77

Replacing in P and S in the last equation:

(H + 2) + (H - 0.73) + H = 8.77

H + 2 + H - 0.73 + H = 8.77

3H + 2 - 0.73 = 8.77

3H + 1.27 = 8.77

3H = 8.77 - 1.27

3H = 7.5

H = 7.5 / 3

H = 2.5

Replacing in the first equation:

P = H + 2

P = 2.5 + 2

P = 4.5

Replacing in the second equation:

S = H - 0.73

S = 2.5 - 0.73

S = 1.77

Veify your values:

P + S + H = 8.77

4.5 + 1.77 + 2.5 = 8.77

So each item is:

Popcorn: $4.5

Soda: $1.77

Hotdog: $2.5