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

#1**+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

#1**+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**+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