Question

A cosmetic company makes three bottles of scented lotion using the recipe shown. Each bottle holds a different amount of lotion. Drag numbers to show how much of each scent should be used in each bottle of lotion.

1/8= vanilla sent
3/8= almond sent
1/2= pineapple sent

bottle 1:
vanilla=?
almond=?
pineapple=4

bottle 2:
vanilla=?
almond=6
pineapple=?


bottle 3:
vanilla=1 1/2
almond=?
pineapple=?

15 PTS!!!!

Answer 1

therefore

Bottle 3

vanilla=1 1/2

almond=4 1/2

pineapple=6Part 1) Bottle 1 (vanilla=1,almond=3,pineapple=4)

Part 2) Bottle 2 (vanilla=2,almond=6,pineapple=8)

Part 3) Bottle 3 (vanilla=1 1/2,almond=4 1/2,pineapple=6)

Explanation:

Let

x ----> the amount of vanilla sent

y ----> amount of almond sent

z ----> the amount of pineapple sent

we know that

so

-----> equation A

-----> equation B

-----> equation C

Part 1) Bottle 1

vanilla=?

almond=?

pineapple=4

we have

Find the value of x

substitute the value of z in equation B

Find the value of y

substitute the value of z in equation C

therefore

Bottle 1

vanilla=1

almond=3

pineapple=4

Part 2) Bottle 2

vanilla=?

almond=6

pineapple=?

we have

Find the value of x

substitute the value of y in equation A

Find the value of z

substitute the value of x in equation B

solve for z

therefore

Bottle 2

vanilla=2

almond=6

pineapple=8

Part 3) Bottle 3

vanilla=1 1/2

almond=?

pineapple=?

we have

convert to an improper fraction

Find the value of y

substitute the value of x in equation A

convert to mixed number

Find the value of z

substitute the value of x in equation B

therefore

Bottle 3

vanilla=1 1/2

almond=4 1/2

pineapple=6

Answer 2

Part 1) Bottle 1 (vanilla=1,almond=3,pineapple=4)

Part 2) Bottle 2 (vanilla=2,almond=6,pineapple=8)

Part 3) Bottle 3 (vanilla=1 1/2,almond=4 1/2,pineapple=6)

Explanation:

Let

x ----> the amount of vanilla sent

y ----> amount of almond sent

z ----> the amount of pineapple sent

we know that

`x:y:z=(1)/(8):(3)/(8):(1)/(2)`

so

`(x)/(y)=(1)/(8):(3)/(8)`

`(x)/(y)=(1)/(3)`

`x=(y)/(3)` -----> equation A

`(x)/(z)=(1)/(8):(1)/(2)`

`(x)/(z)=(1)/(4)`

`x=(1)/(4)z` -----> equation B

`(y)/(z)=(3)/(8):(1)/(2)`

`(y)/(z)=(3)/(4)`

`y=(3)/(4)z` -----> equation C

Part 1) Bottle 1

vanilla=?

almond=?

pineapple=4

we have

`z=4`

Find the value of x

substitute the value of z in equation B

`x=(1)/(4)(4)`

`x=1`

Find the value of y

substitute the value of z in equation C

`y=(3)/(4)(4)`

`y=3`

therefore

Bottle 1

vanilla=1

almond=3

pineapple=4

Part 2) Bottle 2

vanilla=?

almond=6

pineapple=?

we have

`y=6`

Find the value of x

substitute the value of y in equation A

`x=(6)/(3)=2`

Find the value of z

substitute the value of x in equation B

`2=(1)/(4)z`

solve for z

`z=8`

therefore

Bottle 2

vanilla=2

almond=6

pineapple=8

Part 3) Bottle 3

vanilla=1 1/2

almond=?

pineapple=?

we have

`x=1(1)/(2)`

convert to an improper fraction

`x=1(1)/(2)=(1*2+1)/(2)=(3)/(2)`

Find the value of y

substitute the value of x in equation A

`(3)/(2)=(y)/(3)`

`y=(9)/(2)`

convert to mixed number

`y=(9)/(2)=(8)/(2)+(1)/(2)=4(1)/(2)`

Find the value of z

substitute the value of x in equation B

`(3)/(2)=(1)/(4)z`

`z=6`

therefore

Bottle 3

vanilla=1 1/2

almond=4 1/2

pineapple=6