Question 488205: Write an Algebraic Expression for each
1. x years ago, Paul was 20 years old, how old is he now?
2.the sum of a & b, diminished by one-third of c
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1. x years ago, Paul was 20 years old, how old is he now?
let y equal the age that paul is now.
your equation becomes:
y - x = 20
add x to both sides of the equation to get:
y = x + 20
in order to determine what y is, you need to know what x is.
the equation establishes the relationship between y and x, but cannot tell you the value of x.
y depends on x, so x is needed before you can determine y.
for example:
if x = 20, then y = 20 + 20 = 40
if x = 10, then y = 10 + 20 = 30
y will always be 20 more than x but you have no idea of the value of y unless you know the value of x.
2.the sum of a & b, diminished by one-third of c
this would not be an equation.
it would be an expression.
you can make it into an equation by setting it equal to something.
we'll start with the expression
sum of a & b is expressed by (a + b)
if you diminish it by one third of c, then you are subtracting 1/3 of c from it.
the expression becomes:
(a + b) - (1/3)*c
if you want to turn the expression into an equation, then set it equal to something, like the variable y.
you then get:
y = (a + b) - (1/3)*c
example:
let a = 20 and let b = 30 and let c = 120
the sum of a & b is equal to 20 + 30 = 50
if you diminish it by one third of c, then you are diminishing it by 40 because 40 is equal to one third of 120.
if you diminish it by 40, then you are subtracting 40 from it, so you will get 50 - 40 = 10.
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