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Container
A and Container
B are identical. Container
A is
(3)/(4)×-illed with water while Container
B is
(1)/(3)- filled with water. The ratio of the mass of Container
A and its water to the mass of Container
B and its water is
5:3. The mass of the two containers with their water is
1000g. What is the mass of each empty container?

$7$ . Container $A$ and Container $B$ are identical. Container $A$ is $\frac{3}{4} \times$ -illed with water while Container $B$ is $\frac{1}{3}-$ filled with water. The ratio of the mass of Container $A$ and its water to the mass of Container $B$ and its water is $5: 3$ . The mass of the two containers with their water is $1000 \mathrm{~g}$ . What is the mass of each empty container?

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Area of quadrilaterals and triangles: word problems

Full solution

Q.

7

. Container

A

and Container

B

are identical. Container

A

is

\frac{3}{4} \times

-illed with water while Container

B

is

\frac{1}{3}-

filled with water. The ratio of the mass of Container

A

and its water to the mass of Container

B

and its water is

5: 3

. The mass of the two containers with their water is

1000 \mathrm{~g}

. What is the mass of each empty container?

Identify container masses: Let's call the mass of each empty container $m$ . Since the containers are identical, their masses are the same.
Calculate total mass of water: The mass of Container A with water is $5$ parts, and the mass of Container B with water is $3$ parts. Together, they make $5 + 3 = 8$ parts.
Calculate individual container masses: Since the total mass of both containers with water is $1000g$ , each part is $1000g \div 8$ parts $= 125g$ .
Calculate water mass in Container A: Now, the mass of Container A with water is $5$ parts, so it's $5 \times 125\text{g} = 625\text{g}$ .
Calculate water mass in Container B: The mass of Container B with water is $3$ parts, so it's $3 \times 125\text{g} = 375\text{g}$ .
Determine water ratio between containers: Container A is $(\frac{3}{4})$ filled with water, so the water in Container A has a mass of $625\text{g} - m$ .
Set up equation for water masses: Container B is $(\frac{1}{3})$ filled with water, so the water in Container B has a mass of $375g - m$ .
Cross-multiply to solve for m: The ratio of the water in Container A to Container B is the same as the ratio of their total masses, which is $5$ : $3$ . So, ( $625$ \text{g} - m)/( $375$ \text{g} - m) should equal $5$ / $3$ .
Simplify equation to solve for $m$ : Cross-multiply to solve for $m$ : $3(625g - m) = 5(375g - m)$ .
Simplify equation to solve for $\newline$ $m$ : Cross-multiply to solve for $\newline$ $m$ : $\newline$ $3(625g - m) = 5(375g - m)$ .This simplifies to $\newline$ $1875g - 3m = 1875g - 5m$ .
Simplify equation to solve for $m$ : Cross-multiply to solve for $m$ : $3(625g - m) = 5(375g - m)$ .This simplifies to $1875g - 3m = 1875g - 5m$ .Rearrange the equation to solve for $m$ : $2m = 1875g - 1875g$ .

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