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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

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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

#1
+19620
+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
+19620
+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
#2
+17744
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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