Mathematics, 02.08.2019 03:30 shayhiddinovxasan93

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? show your work with your answer!

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Answer from: Faber9714

Let

be the chocolate chip cookies, so the peanut butter treats will be 144-x

.
We know that the cookies and the treats are in a ratio of 5:3, so: $\frac{cookies}{treats} = \frac{5}{3} = \frac{x}{144-x}$
Now we can solve for

:
$\frac{5}{3} = \frac{x}{144-x}$
5(144-x)=3x

$x= \frac{720}{8}$
x=90

We now know Lydia has 90 chocolate chip cookies, and 144-x=144-90=54

peanut butter treats.

Then, Lydia's friend ate $\frac{3}{5}$ of her cookies, so her friend ate $\frac{2}{5} (90)=36$ cookies. Therefore, Lydia has 90-36=54

cookies left.
Now we can calculate the total amount of baked goods after her friend ate the cookies:
144-54=90

Therefore, our remainder treats will be:
90-x

We also now that after her friend ate 54 cookies and some treats, the new ratio is 6:1, and that's all we need to set up our new equation and solve it to find how many treats she ate:
$\frac{cookies}{treats} = \frac{6}{1} = \frac{54}{90-x}$
6(90-x)=54

$x= \frac{486}{6}$
x=81

Finally, if she ate 81 out 90 treats, we can conclude the Lydia has left with 9 peanut butter treats.

Answer from: hihihi129473838

Let:
x: chip cookies
y: peanut butter
We have the following system of equations:
x + y = 144
x / y = 5/3
We solve the system of equations:
Step 1:
x + y = 144
y = (3/5) x
Step 2:
x + (3/5) x = 144
(8/5) x = 144
x = (5/8) * (144) = 90
Step 3:
y = (3/5) x
y = (3/5) * (90) = 54
Lydia's friends ate 2/5 of her chocolate chip cookies:
x '= (2/5) * (90) = 36
the cookies outnumbered the treats 6 to 1
x '/ y' = 6/1
Clearing y '
y '= (1/6) * x'
y '= (1/6) * 36
y '= 6

she had left 6 butter treats

Answer from: Quest

He is right i did this thing before

Answer from: Quest

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

= $\sqrt{(9-6)^{2} +(12-6)^{2} } \\=\sqrt(45)=3\sqrt(5)$

side j'k'=distance between j' and k'

= $\sqrt{(3-2)^{2} +(2-4)^{2} } \\=sqrt(5)$

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

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