Respuesta :
Answer:
She buy 7 oatmeal raisin cookies.
Step-by-step explanation:
Given:
Tasty bakery sells three kinds of cookies Chocolate chip at $.30 each oatmeal raisin at $.35 each and peanut butter at $.40 each.
She buys some of each kind and chooses twice as many peanut butters as chocolate chip.
If she spends $5.75 on 16 cookies.
Now, to find the quantity of oatmeal raisin cookies she buy.
Let the quantity of oatmeal raisin cookies be [tex]x.[/tex]
And let the quantity of Chocolate chip cookies be [tex]y[/tex].
So, the quantity of peanut butter cookies is [tex]2y.[/tex]
Now, the total quantity of cookies:
[tex]x+y+2y=16\\\\x+3y=16\\\\x=16-3y\ \ \ \ .....(1)[/tex]
Now, the total money she spends on buying cookies:
[tex]0.30(y)+0.35(x)+0.40(2y)=5.75[/tex]
Substituting the value of [tex]x[/tex] from equation (1):
[tex]0.30(y)+0.35(16-3y)+0.40(2y)=5.75\\\\0.30y+5.6-1.05y+0.80y=5.75\\\\5.6+0.05y=5.75[/tex]
Subtracting both sides by 5.6 we get:
[tex]0.05y=0.15[/tex]
Dividing both sides by 0.15 we get:
[tex]y=3.[/tex]
The quantity of Chocolate chip cookies = 3.
Now, to substitute the value of [tex]y[/tex] in equation (1) to get the quantity of oatmeal raisin cookies:
[tex]x=16-3y\\\\x=16-3(3)\\\\x=16-9\\\\x=7.[/tex]
The quantity of oatmeal raisin cookies = 7.
Therefore, she buy 7 oatmeal raisin cookies.
