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The ratio of the mass of the sugar in packet A to the mass of the sugar in packet B is 5 is to 6.After the mass of the sugar in packet A is increase by 30 percent. By what percentage must the mass of the sugar in packet B be decrease so that the total mass of sugar in packet A and B remain the same?

Guest Jul 13, 2015

Best Answer 

 #1
avatar+18946 
+10

The ratio of the mass of the sugar in packet A to the mass of the sugar in packet B is 5 is to 6.After the mass of the sugar in packet A is increase by 30 percent. By what percentage must the mass of the sugar in packet B be decrease so that the total mass of sugar in packet A and B remain the same ?

 

$$\\\small{\text{
$A:B= 5:6 $ ~~or~~ $B=\dfrac{6}{5}A$ ~~or ~~ $A=\dfrac{5}{6}B$
}}\\\\
\small{\text{
total mass of sugar in packet A and B: $\qquad A+B= A+ \dfrac{6}{5}A = \dfrac{11}{5}A$
}}\\\\
\small{\text{
increase $A = a \qquad a = 1.3\cdot A$
}}\\
\small{\text{
decrease $ B = b$
}}\\
\small{\text{
total mass of sugar in packet a and b: $\qquad a+b=A+B=\dfrac{11}{5}A$
}}\\
\small{\text{$
\begin{array}{rcl}
a+b&=&\dfrac{11}{5}A \\\\
1.3\cdot A +b &=&\dfrac{11}{5}A \\\\
b &=& \dfrac{11}{5}A - 1.3\cdot A\\\\
\mathbf{b} & \mathbf{=} & \mathbf{0.9 \cdot A}\qquad | \qquad A=\dfrac{5}{6}B \\\\
b &=& 0.9 \cdot \dfrac{5}{6}B \\\\
\mathbf{b} & \mathbf{=} & \mathbf{0.75 \cdot B }
\end{array}
$ }}\\$$

 

sugar in packet B be decrease  25 %

 

heureka  Jul 13, 2015
Sort: 

2+0 Answers

 #1
avatar+18946 
+10
Best Answer

The ratio of the mass of the sugar in packet A to the mass of the sugar in packet B is 5 is to 6.After the mass of the sugar in packet A is increase by 30 percent. By what percentage must the mass of the sugar in packet B be decrease so that the total mass of sugar in packet A and B remain the same ?

 

$$\\\small{\text{
$A:B= 5:6 $ ~~or~~ $B=\dfrac{6}{5}A$ ~~or ~~ $A=\dfrac{5}{6}B$
}}\\\\
\small{\text{
total mass of sugar in packet A and B: $\qquad A+B= A+ \dfrac{6}{5}A = \dfrac{11}{5}A$
}}\\\\
\small{\text{
increase $A = a \qquad a = 1.3\cdot A$
}}\\
\small{\text{
decrease $ B = b$
}}\\
\small{\text{
total mass of sugar in packet a and b: $\qquad a+b=A+B=\dfrac{11}{5}A$
}}\\
\small{\text{$
\begin{array}{rcl}
a+b&=&\dfrac{11}{5}A \\\\
1.3\cdot A +b &=&\dfrac{11}{5}A \\\\
b &=& \dfrac{11}{5}A - 1.3\cdot A\\\\
\mathbf{b} & \mathbf{=} & \mathbf{0.9 \cdot A}\qquad | \qquad A=\dfrac{5}{6}B \\\\
b &=& 0.9 \cdot \dfrac{5}{6}B \\\\
\mathbf{b} & \mathbf{=} & \mathbf{0.75 \cdot B }
\end{array}
$ }}\\$$

 

sugar in packet B be decrease  25 %

 

heureka  Jul 13, 2015
 #2
avatar+17711 
+5

We don't need the actual masses, we can use just their ratios to get the answer. 

mass(A)/mass(B)  =  5/6 

increasing mass(A) by 30%:  5 x 1.3  =  6.5   (an increase of 1.5)

Since the total mass of A and B is 11, to keep the total mass the same, the mass of B must be decreased by 1.5 down to 4.5.

1.5, in comparison to 6, is a decrease of 25%

geno3141  Jul 13, 2015

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