#### Solution for 42 is what percent of 120:

42:120*100 =

(42*100):120 =

4200:120 = 35

Now we have: 42 is what percent of 120 = 35

Question: 42 is what percent of 120?

Percentage solution with steps:

Step 1: We make the assumption that 120 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\%}={120}.

Step 4: In the same vein, {x\%}={42}.

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

{100\%}={120}(1).

{x\%}={42}(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{120}{42}

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

\frac{x\%}{100\%}=\frac{42}{120}

\Rightarrow{x} = {35\%}

Therefore, {42} is {35\%} of {120}.

#### Solution for 120 is what percent of 42:

120:42*100 =

(120*100):42 =

12000:42 = 285.71

Now we have: 120 is what percent of 42 = 285.71

Question: 120 is what percent of 42?

Percentage solution with steps:

Step 1: We make the assumption that 42 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\%}={42}.

Step 4: In the same vein, {x\%}={120}.

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

{100\%}={42}(1).

{x\%}={120}(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{42}{120}

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

\frac{x\%}{100\%}=\frac{120}{42}

\Rightarrow{x} = {285.71\%}

Therefore, {120} is {285.71\%} of {42}.

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