OpenStudy (thecatman):

One week, Huang ordered 1 pizza and 2 sodas for $12. The next week, he ordered 3 pizzas and 4 sodas from the same restaurant for $30. Write and graph a system of equations to determine the cost of each pizza and the cost of each soda from this restaurant. Let x = the cost of a pizza Let y = the cost of a soda A pizza costs $8 and a soda costs $4. A pizza costs $6 and a soda costs $3. Individual costs cannot be determined. There is no solution. There are many possible costs for each. There are infinitely many solutions.

3 years ago
OpenStudy (thecatman):

@doc.brown

3 years ago
OpenStudy (thecatman):

i think b

3 years ago
OpenStudy (doc.brown):

1 pizza plus 2 sodas is $12 3 pizzas plus 4 sodas is $30 Let x = the cost of a pizza Let y = the cost of a soda

3 years ago
OpenStudy (thecatman):

so would it be B

3 years ago
OpenStudy (doc.brown):

\[1x+2y=12\]\[3x+4y=30\]

3 years ago
OpenStudy (thecatman):

by your calculations i would say yes because pizzas= 6 and sodas= 3 when add i pizza and two sodas you get 12

3 years ago
OpenStudy (doc.brown):

\[1x+2y=12\]\[1x=12-2y\] Does that seem reasonable? 1 pizza is $12 minus the cost of 2 sodas.

3 years ago
OpenStudy (thecatman):

? now i'm confused

3 years ago
OpenStudy (doc.brown):

Does this makes logical sense?\[1x+2y=12\]

3 years ago
OpenStudy (thecatman):

yes

3 years ago
OpenStudy (doc.brown):

If I subtract the cost of 2 sodas from both sides i get\[1x+2y=12\]\[1x+2y-2y=12-2y\]2y-2y is 0 so\[1x=12-2y\]

3 years ago
OpenStudy (thecatman):

sorry i had to put my pet away

3 years ago
OpenStudy (doc.brown):

That's what she said.

3 years ago
OpenStudy (thecatman):

ok

3 years ago
OpenStudy (thecatman):

ha ha you got me

3 years ago
OpenStudy (yanasidlinskiy):

A pizza costs $6 and a soda costs $3

3 years ago
OpenStudy (thecatman):

thanks

3 years ago
OpenStudy (yanasidlinskiy):

np:)anytime

3 years ago
OpenStudy (doc.brown):

You know one pizza is 12-2y, so now 3 pizzas are 3(12-2y) I'll stick it in your second equation.\[3x+4y=30\]\[3(12-2y)+4y=30\]\[36-6y+4y=30\]\[36-30=6y-4y\]\[2y=6\]\[y=3\]

3 years ago