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
Accepted Solution
A:
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: