Question

Alfred collects black and brown socks but loses a lot of them. If 60% of all his socks are brown, 20% of his brown socks are in the wash and 120 brown socks are in his sock drawer, how many socks does Alfred have?

Answer 1

Answer:

Alfred has 250 socks in his collection.

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

Based on the information given to us we can see that out of All his Brown socks he has 20% in the wash and the rest are in his drawer. Meaning 80% of the Brown socks are in his drawer. So we first need to find how many Brown socks are in the wash. We can solve this using the Rule of Three property as shown in the picture below.

120 drawer   ⇒   80%

      x wash    ⇒  20%

$\frac{120*20}{80} = 30$

Now that we have the amount of Brown socks in the washer we can add that to the amount in the drawer to find the total amount of Brown socks.

$Br = 120+30\\Br = 150$

So we now know that there are a total of 150 Brown socks. Since the question states that the Brown socks are 60% of the total we can use the Rule of Three to find the total.

150 Brown   ⇒   60%

    T  Total   ⇒   100%

$\frac{150*100}{60} = T$

$250 socks = T$

Finally, we can see that Alfred has 250 socks in his collection.

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