#### Solution for 77 is what percent of 40:

77:40*100 =

(77*100):40 =

7700:40 = 192.5

Now we have: 77 is what percent of 40 = 192.5

Question: 77 is what percent of 40?

Percentage solution with steps:

Step 1: We make the assumption that 40 is 100% since it is our output value.

Step 2: We next represent the value we seek with {x}.

Step 3: From step 1, it follows that {100\%}={40}.

Step 4: In the same vein, {x\%}={77}.

Step 5: This gives us a pair of simple equations:

{100\%}={40}(1).

{x\%}={77}(2).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have

\frac{100\%}{x\%}=\frac{40}{77}

Step 7: Taking the inverse (or reciprocal) of both sides yields

\frac{x\%}{100\%}=\frac{77}{40}

\Rightarrow{x} = {192.5\%}

Therefore, {77} is {192.5\%} of {40}.

#### Solution for 40 is what percent of 77:

40:77*100 =

(40*100):77 =

4000:77 = 51.95

Now we have: 40 is what percent of 77 = 51.95

Question: 40 is what percent of 77?

Percentage solution with steps:

Step 1: We make the assumption that 77 is 100% since it is our output value.

Step 2: We next represent the value we seek with {x}.

Step 3: From step 1, it follows that {100\%}={77}.

Step 4: In the same vein, {x\%}={40}.

Step 5: This gives us a pair of simple equations:

{100\%}={77}(1).

{x\%}={40}(2).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have

\frac{100\%}{x\%}=\frac{77}{40}

Step 7: Taking the inverse (or reciprocal) of both sides yields

\frac{x\%}{100\%}=\frac{40}{77}

\Rightarrow{x} = {51.95\%}

Therefore, {40} is {51.95\%} of {77}.

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