Answer asap-lydia baked a total of 144 chocolate chip cookies and peanut butter treats for valentine's day. initially, the ratio of chocolate chip cookies to peanut butter treats was 5: 3. after lydia's friends ate 2/5 of her chocolate chip cookies and some of her peanut butter treats, the cookies outnumbered the treats 6 to 1. how many peanut butter treats did she have left? open

The correct answer is:

9 peanut butter treats.

Explanation:

The ratio of chocolate chip cookies to peanut butter treats is 5:3. We can use this to set up a proportion, letting c be chocolate chip cookies and p be peanut butter treats:
c/p = 5/3.

Cross multiplying, we get the equation
c*3=p*5
3c=5p.

Isolating c by dividing by 3, we have
3c/3 = 5p/3
c=5/3p.

We know that the total number of items baked were 144:
p+c=144.

Substituting 5/3p for c, we have
p+5/3p=144.

p = 3/3p, so this gives us
3/3p+5/3p = 144
8/3p=144.

Dividing both sides by 8/3:
(8/3p)/(8/3) = 144/(8/3).

When we divide fractions, we flip the second one and multiply:
p=144*(3/8) = 432/8 = 54.

She baked 54 peanut butter treats.

Plugging this into the equation for the total amount of items,
54+c=144

Subtract 54 from both sides:
54+c-54=144-54
c=90.

She baked 90 chocolate chip cookies.

Since her friends ate 2/5 of the chocolate chip cookies, she has 1-2/5=3/5 of them left:
3/5 of 90 = 3/5(90) = 3/5(90/1) = 270/5 = 54.

She has 54 chocolate chip cookies left.

We do not know how many peanut butter treats her friends ate, so we will use x to represent this and rewrite our ratio:
54-x (since she had 54 treats and her friends ate an unknown amount) over 54 (since she has 54 chocolate chip cookies left) equals the ratio 1 to 6:

(54-x)/54 = 1/6.

Cross multiply:
(54-x)*6=54*1
54*6-x*6=54
324-6x=54.

Subtract 324 from both sides:
324-6x-324=54-324
-6x=-270.

Divide both sides by -6:
-6x/-6=-270/-6
x=45.

Her friends ate 45 of her peanut butter treats; this leaves her with 54-45=9.