Pls help me to understand this math answer.
One day, Fida decided to give half of her dolls to Melika. The day after, she decided to give 3 more dolls to Melika. Fida now only has 3/8 of the dolls she had before. How many dolls did she have originally?
So, I wrote 3 dolls =1/8, because 3/8+1/8= 4/8=1/2, but answer is 24. I don't understand why there is multiplication of 3*8 in answer? Pls may you help me to understand that.
You are studying algebra, so learn how to use it.
First, assign
in writing a
unique symbol to
each potentially relevant number that is
unknown.
\(\displaystyle x = \text { original number of dolls Fida had.}\)
\(\displaystyle y = \text { number of dolls Fida had after first gift.}\)
\(\displaystyle z = \text { number of dolls Fida had after second gift.}\)
You have three unknowns so you need three equations.
Fida decided to give half of her dolls to Melika \(\displaystyle \implies y = x - \dfrac{1}{2} * x = \dfrac{1}{2} * x.\)
she gave 3 more dolls to Melika\(\displaystyle \implies z = y - 3 = \dfrac{1}{2} * x - 3.\)
Fida now only has 3/8 of the dolls she had before \(\displaystyle \implies z = \dfrac{3}{8} * x.\)
Now z is certainly equal to itself so
\(\displaystyle z = z \implies \dfrac{1}{2} * x - 3 = \dfrac{3}{8} * x.\)
Fractions are a pain in the neck. Have you ever been taught how to "clear fractions."
You multiply
both sides of your equation by the
lowest common multiple of the
denominators of the fractions in the equation.
What is the lowest common multiple of the denominators of 1/2 and 3/8? 8 of course. So
\(\displaystyle 8 * \left ( \dfrac{1}{2} * x - 3 \right ) = 8 * \left ( \dfrac{3}{8} * x \right ) \implies \\
\dfrac{8}{2} * x - 8 * 3 = \dfrac{8 * 3}{8} * x \implies
4x - 24 = 3x \implies 4x - 24 + 24 = 3x + 24 \implies 4x = 3x + 24 \implies \\
-\ 3x + 4x = -\ 3x + 3x + 24 \implies x = 24 \implies y = \dfrac{1}{2} * x = 12 \implies \\
z = y - 3 = 12 - 3 = 9.\)
Let's check. \(\displaystyle \dfrac{3}{8} * 24 = 3 * \dfrac{24}{8} = 3 * 3 = 9.\)
Is it clear now? Multiplying
everything by 8 got rid of those
nasty fractions.