Question

Amy wants to sell at most 25 cookies and at least 10 sprites

per day. She profits $.50 on every cookie and $1.00 on every
sprite. She wants to earn at least $ 30 per day. Which of the
following systems of inequalities represents this scenario?
A. X + x 225
B.xs 25
.50x + y 2 30
y? 10
x + y 230
C. x < 25
Y 2 10
.50x + y 2 30
D. x < 25
y> 10
.50x + y > 30​

Answer 1

`x\leq 25\\y\geq 10\\.50x + y\geq 30`

Explanation:

It is given that,

Amy wants to sell at most 25 cookies ,

Let number of cookies be '
`x`' , then
`x` should be less than or equal to 25

Which is represented by
`x\leq 25` ,

Further,

Let number of sprites be '
`y`', then '
`y`' should be greater than or equal to 10

Which is represented by
`y\geq 10`

Also,

Given,

she profits $.50 on every cookie

and $1.00 on every sprite.

So total profit on selling cookies would be

= Profit on each cookie times the number of cookies

=
`.50* x`

=
`.5x`

Similarly, total profit on selling sprites would be

=profit on each sprite times the number of sprites

=
`1.00* y`

=
`y`

Now, combining these two should be greater than or equal to $30

representing this through an equation,

`.50x+y\geq 30`

Thus the sysytem of equations is given as:

`x\leq 25\\y\geq 10\\.50x + y\geq 30`