Answer:
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)
Step-by-step explanation:
Let
x ----> the amount of vanilla sent
y ----> amount of almond sent
z ----> the amount of pineapple sent
we know that
[tex]x:y:z=\frac{1}{8}:\frac{3}{8}:\frac{1}{2}[/tex]
so
[tex]\frac{x}{y}=\frac{1}{8}:\frac{3}{8}[/tex]
[tex]\frac{x}{y}=\frac{1}{3}[/tex]
[tex]x=\frac{y}{3}[/tex] -----> equation A
[tex]\frac{x}{z}=\frac{1}{8}:\frac{1}{2}[/tex]
[tex]\frac{x}{z}=\frac{1}{4}[/tex]
[tex]x=\frac{1}{4}z[/tex] -----> equation B
[tex]\frac{y}{z}=\frac{3}{8}:\frac{1}{2}[/tex]
[tex]\frac{y}{z}=\frac{3}{4}[/tex]
[tex]y=\frac{3}{4}z[/tex] -----> equation C
Part 1) Bottle 1
vanilla=?
almond=?
pineapple=4
we have
[tex]z=4[/tex]
Find the value of x
substitute the value of z in equation B
[tex]x=\frac{1}{4}(4)[/tex]
[tex]x=1[/tex]
Find the value of y
substitute the value of z in equation C
[tex]y=\frac{3}{4}(4)[/tex]
[tex]y=3[/tex]
therefore
Bottle 1
vanilla=1
almond=3
pineapple=4
Part 2) Bottle 2
vanilla=?
almond=6
pineapple=?
we have
[tex]y=6[/tex]
Find the value of x
substitute the value of y in equation A
[tex]x=\frac{6}{3}=2[/tex]
Find the value of z
substitute the value of x in equation B
[tex]2=\frac{1}{4}z[/tex]
solve for z
[tex]z=8[/tex]
therefore
Bottle 2
vanilla=2
almond=6
pineapple=8
Part 3) Bottle 3
vanilla=1 1/2
almond=?
pineapple=?
we have
[tex]x=1\frac{1}{2}[/tex]
convert to an improper fraction
[tex]x=1\frac{1}{2}=\frac{1*2+1}{2}=\frac{3}{2}[/tex]
Find the value of y
substitute the value of x in equation A
[tex]\frac{3}{2}=\frac{y}{3}[/tex]
[tex]y=\frac{9}{2}[/tex]
convert to mixed number
[tex]y=\frac{9}{2}=\frac{8}{2}+\frac{1}{2}=4\frac{1}{2}[/tex]
Find the value of z
substitute the value of x in equation B
[tex]\frac{3}{2}=\frac{1}{4}z[/tex]
[tex]z=6[/tex]
therefore
Bottle 3
vanilla=1 1/2
almond=4 1/2
pineapple=6
