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Pat and Sally had a total of 23 gel pens. Pat had 7 more than sally. how many gel pens did sally have?

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2 Answers

This instructs you in turning word problems into mathematical (algebraic) expressions that you can solve.
 
Let's define the variable P as the number of pens that Pat has (it's often easy to use the names to get the variables).
 
Similarly, S is the variable for the number of pens Sally has.
 
The total (sum, addition of two parts) of pens between Pat and Sally is 23.  So this gives us one equation:  P + S = 23
 
We have two unknowns.  In algebra, it is a fact that in order to solve the unknowns, you need the same number of equations with those unknowns.  Thus we have two unknowns, and we need two equations.  We thus need another equation.
 
We are given the information that the number of pens Pat has is 7 more than Sally.  The equation P = S + 7 describes that.  We now have two equations!
 
1.  P + S = 23
2.  P = S + 7
 
We can substitute the value of P in equation 1 from the value in equation 2.
 
A.  S + 7 + S = 23
 
Now we can solve for S:
 
B.   2S = 16
Note that I know that S + S = 2S, and I subtracted 7 from both sides of the equation to get the constants on one side.  Now divide by 2 on both sides:
 
C.  S = 8.
 
Thus Sally has 8 pens.  Since Pat had 7 more, we know that Pat has 8 + 7 = 15 pens.
 
To verify our results, we recall Pat and Sally both had 23 pens total, and 8 + 15 certainly adds up to 23.
 
Hi Christian;
x=quantity of Sally's pens
23=Sally's pens plus Pat's pens.
23=x+(x+7)
23=2x+7
Let's subtract 7 from both sides...
-7+23=2x+7-7
16=2x
8=x=Sally's pens
23-8=15=Pat's pens