Translate this statement into an equation: M has five times as many quarters as s.
In this equation, you have two variables. One stands for the number of quarters that M has and one stands for the number of quarters that S has. You can name these variables whatever you like, but we might as well call them M and S. So those stand for the number of quarters each has.
We know that M has 5 times as many as S. So we write the following equation:
M = 5S (Remember that 5S means 5 times S)
This makes sense because what this equation says is that the number of quarters M has (M) is equal to 5 times the number that S has (5S).
M had five times as many quarters as S.
Let S has x quarters:
Then S = x quarters
Let M has y quarters.
==> M = y quarters.
But M has 5 times the quarters.
M = 5*S
y = 5*x
'has' means equal.
Therefore, you get ...
M has five times as many quarters as s.
We have two variables here: M for the first person and s for the second person.
The phrase "five times as many as s" denotes multiplication ---> 5s
M has this much so we can set M equal to this value:
M = 5s
M has five times as many quarters as s
M has 5 times as many quarters as S.
To convert thi above statement into an equation we proceed as follows:
First we pressume M have x quarters and S have y quarters.
By the information that M has 5 times as many quarters as S has, we get a relation between x and y:
x = 5y .
Here x and y are two variables.
The equation is also called the linear equation, as the varibles are in degree 1.
The other equivalent relations (or equation) are:
x-y = 0 , or y-x = 0 , or 0 = x-y.
To solve x and y we need two indepedent equations.