One number is 6 more than another. The difference between their squares is 204. What are the numbers?
2 answers:
Answer: 20 and 14
Step-by-step explanation:
Using a little guess and check, we can figure out that the numbers are 6 apart and the difference between their squares is 204.
A trick to doing this is to start with a number that is easily squared like 10 or 20 and see if the difference between their numbers is larger or smaller and change your numbers based on them.
Hope this helped :)
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Let's go through this problem step by step while bearing in mind the concept of PEMDAS.
Step 1:
Declaration of the expression. Nothing wrong here yet.
Step 2:
Clarise evaluated what's inside the parenthesis first - which was the right thing to do! There are no mistakes in this step.
Step 3:
In this step she subtracted first. This should not be the case! PEMDAS tells us that the exponents and division gets higher priority than subtraction. This is therefore the first mistake Clarise makes.
Step 4:
In this step Clarise evaluates the exponent. This does not violate any rules (relative to the previous expression) since PEMDAS tells us that exponents take higher priority than division.
Step 5:
(Clarise's final answer)
In Clarise's final step, she manages to get the wrong answer! Dividing 51.68 by 0.16 would give us 323. This is another mistake of Clarise.
Looking at the choices, we can now identify what mistakes Clarise made:
-She subtracted before evaluating the exponents
-She subtracted before she divided
-She divided incorrectly
Step 1:
Declaration of the expression. Nothing wrong here yet.
Step 2:
Clarise evaluated what's inside the parenthesis first - which was the right thing to do! There are no mistakes in this step.
Step 3:
In this step she subtracted first. This should not be the case! PEMDAS tells us that the exponents and division gets higher priority than subtraction. This is therefore the first mistake Clarise makes.
Step 4:
In this step Clarise evaluates the exponent. This does not violate any rules (relative to the previous expression) since PEMDAS tells us that exponents take higher priority than division.
Step 5:
In Clarise's final step, she manages to get the wrong answer! Dividing 51.68 by 0.16 would give us 323. This is another mistake of Clarise.
Looking at the choices, we can now identify what mistakes Clarise made:
-She subtracted before evaluating the exponents
-She subtracted before she divided
-She divided incorrectly