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

the 1st digit is in the 100s n its 1

step-by-step explanation:

3,589÷18 = 199.389

so the first digit of the quotient is in the 100s n its 1

Answer from: Quest

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

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