Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4:3. What is the ratio of the composition of the two basic elements in alloy X?
1:1
2:3
5:2
4:3
Explanation:
The new alloy X is formed from the two alloys A and B in the ratio 4:3.
Hence, 7 parts of the alloy contains 4 parts of alloy A and 3 parts of alloy B.
Let 7x ounces of alloy X contain 4x ounces of alloy A and 3x ounces of alloy B.
Now, alloy A is formed of the two basic elements mentioned in the ratio 5:3.
Hence, 4x ounces of alloy A contains
$\left(\dfrac{5}{5+3}\right)4x=\dfrac{5x}{2}$ ounces of first basic element
and $\dfrac{3}{5+3}4x=\dfrac{3x}{2}$ ounces of the second basic element.
Also, alloy B is formed of the two basic elements mentioned in the ratio 1:2.
Hence, let the 3x ounces of alloy A contain $\left(\dfrac{1}{1+2}\right)$3x=x ounces of the second basic
element. ounces of the first basic element and $\left(\dfrac{2}{1+2}\right)$3x=2x ounces of the second basic element.
Then the total compositions of the two basic elements in the 7x ounces of alloy X would contain
$\dfrac{5x}{2}$ ounces (from A) + x ounces (from B) = $\dfrac{7x}{2}$ ounces of first basic element,
and basic elements in alloy X is $\dfrac{3x}{2}$(from A) + 2x(from B) = $\dfrac{7x}{2}$ ounces of the second basic element.
Hence, the composition of the two basic elements in alloy X
is $\dfrac{7x}{2}:\dfrac{7x}{2}$=1:1
The new alloy X is formed from the two alloys A and B in the ratio 4:3.
Hence, 7 parts of the alloy contains 4 parts of alloy A and 3 parts of alloy B.
Let 7x ounces of alloy X contain 4x ounces of alloy A and 3x ounces of alloy B.
Now, alloy A is formed of the two basic elements mentioned in the ratio 5:3.
Hence, 4x ounces of alloy A contains
$\left(\dfrac{5}{5+3}\right)4x=\dfrac{5x}{2}$ ounces of first basic element
and $\dfrac{3}{5+3}4x=\dfrac{3x}{2}$ ounces of the second basic element.
Also, alloy B is formed of the two basic elements mentioned in the ratio 1:2.
Hence, let the 3x ounces of alloy A contain $\left(\dfrac{1}{1+2}\right)$3x=x ounces of the second basic
element. ounces of the first basic element and $\left(\dfrac{2}{1+2}\right)$3x=2x ounces of the second basic element.
Then the total compositions of the two basic elements in the 7x ounces of alloy X would contain
$\dfrac{5x}{2}$ ounces (from A) + x ounces (from B) = $\dfrac{7x}{2}$ ounces of first basic element,
and basic elements in alloy X is $\dfrac{3x}{2}$(from A) + 2x(from B) = $\dfrac{7x}{2}$ ounces of the second basic element.
Hence, the composition of the two basic elements in alloy X
is $\dfrac{7x}{2}:\dfrac{7x}{2}$=1:1