Answer:
Clara's number is 42 less than Anna's number
Step-by-step explanation:
We can start this problem out by setting our variables up:
A= Anna's number
B= Boris's number
C= Clara's number
so we can use them to build our equations. We can sepparate the problem into little more understandable pieces of information, let's start with the first piece of information:
- "Ana's number increased by 20"
A+20
- "boris's number decreased by 22"
B-22
- "21 greater than boris's number decreased by 22."
(B-22)+21
- "Ana's number increased by 20 is 21 greater than boris's number decreased by 22."
A+20=(B-22)+21
This is our first important equation here. Let's go with the second part of the problem:
- "Boris's number decreased by 20"
B-20
- "claras number increased by 22"
C+22
- "21 greater than claras number increased by 22"
(C+22)+21
Now the whole thing:
"Boris's number decreased by 20 is 21 greater than claras number increased by 22."
B-20=(C+22)+21
This is our second important equation.
So now we have the following system of equations:
A+20=(B-22)+21
B-20=(C+22)+21
We can now simplify the equations by combining like terms so we get:
Equation 1:
A+20=(B-22)+21
we can get rid of the parenthesis so we get:
A+20=B-22+21
We can subtract a 20 from both sides of the equation so we get:
A=B-22+21-20
We perform the subtractions so we get:
A=B-21
Equation 2:
B-20=(C+22)+21
We get rid of the parenthesis:
B-20=C+22+21
We add a 20 to both sides so we get:
B=C+22+21+20
We can now perform the additions so we get:
B=C+63
And now we can combine the equations. In this case we can substitute equation 2 into equation 1 to get:
A=C+63-21
We combine like terms to get:
A=C+42
We can subtract 42 from both sides to get:
C=A-42
which reads:
Clara's number is 42 less than Anna's number.
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