Question

the computer club has a budget of $90 for a pizza party. the club can get large pizzas for $10 and cases of soda for $3.50. the club would like to buy at least 5 large pizza and at least 3 cases of soda.
write a system of linear inequality that describes the given information. use X for the number of large pizzas and Y for the number of cases of soda the club will buy.graph the system you wrote in part(a).can the club buy 6 pizzas and 4 cases of
soda?explain. find the maximum number of cases of soda the club can buy if the club decides to buy 7 pizzas

Answer 1

Are asking for an equation?

Answer 2

yes

Answer 3

(5*10) + (3*3.50) =?
10x + 3y = ?

Answer 4

That what i would put

Answer 5

any ideas?

bear in mind that their budget is only $90

Answer 6

The goal here is the club wants to keep the budget somehow $ 90 or below. Since x will be pizza and y will be soda then system linear inequality will be \[5x + 3.5y \le 90\]So from here you just plug in x =5 for pizza and y = 3 for sodas. If that is less than or equal to 90 then it works because it fits their budget. Same with answering part a.) just plug in the values x and y.

Last one you have to solve for y because you trying to find the maximum amount of sodas you can buy when buying 7 pizzas.
\[ \frac{ 90 -10x}{3.5} = y\] Plug in the values\[\frac{ 90-(10*7) }{ 3.5 } = 5.7142\]We neea whole number we cannot buy 5.7 cases of soda. If we round up to 6 and then you plug in 6 and 7 int othe equation you will get 91 which is not right because the inequality says it must be equal to 90 or less. So we round do to 5 as the nearest whole number. If we do that then the actual total cost will be 87.50 which is less than 90. So that works.

Answer 7

Small error the equations should be \[\frac{ 90 -10x }{ 3.5 }\le y\]\[\frac{ 90 - (10*7) }{ 3.5 } \le y\]. It should be no equal signs since this is a inequality.