Question

Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeved shirts are $10 each and short-sleeved shirts are $5 each. The club can spend no more than $165. What are the minimum and maximum numbers of long-sleeved shirts that can be purchased?
A minimum of ___ long-sleeved shirts can be purchased.
A maximum of ___ long-sleeved shirts can be purchased.

Answer 1

0
8
-----------------------------------------------------------------------

Answer 2

Answer:

Maximum number of long sleeved shirt that can be purchase is, 8

and

Minimum number of long sleeved shirt that can be purchased is, 0

Step-by-step explanation:

let y represents the number of short sleeves  and x represents the number of long sleeves.

As per the given condition:

Members of a school club are buying matching shirts. They know at least 25 members will get a shirt.

we have;

$x+y\geq 25$              or

$y\geq 25 -x$    ....[1]

Since, long sleeves shirt are $ 10 each and short sleeves shirt are $ 5 each.

then;

Total cost of long sleeves is 10x and

the total cost of short sleeves is 5y

Also; the club can spend no more than $ 165

then;

$10x+5y\leq 165$                  

 $5y\leq 165 -10x$ or

$y\leq 33-2x$ ......[2]

Solving the inequality equation with the graph :

Plot equation [1] and [2]; we get the maximum at point (8 , 17)

so, x= 8.

If we take minimum value of x =0 then y is between 25 and 33.

so, the solution area is between the lines to the left of where the lines intersect.

Therefore, the maximum number of long sleeved shirts can be purchased is 8 and the minimum number of long sleeved shirt can be purchased is 0