Respuesta :
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.
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.
Answer:
Lydia was left with 9 peanut butter treats.
Step-by-step explanation:
Let the chocolate chip cookies be = x
so the peanut butter treats will be = 144-x
Given ,the cookies and the treats are in a ratio of 5:3.
So, [tex]\frac{x}{144-x}=\frac{5}{3}[/tex]
[tex]3x=(144-x)5[/tex]
This gives x=90
As Lydia has 90 chocolate chip cookies, so, the number of peanut butter treats = 144-x = 144-90 = 54
Now, Lydia's friend ate 2/5 of her cookies, it becomes =
[tex]\frac{2}{5}*90= 36[/tex]
Therefore, Lydia has 90-36=54 cookies left.
Now the total amount of baked goods remains = 144-54=90
Hence, remainder treats will be = 90-x
The new ratio is 6:1
So, [tex]\frac{54}{90-x}=\frac{6}{1}[/tex]
[tex]54=6(90-x)[/tex]
This gives x = 81
Hence, after eating 81 out 90 treats,Lydia is left with = 90-81 = 9 peanut butter treats.
