John has x dollars more than Peter has, and together they have a total of y dollars.
John has x dollars more than Peter has, and together they have a total of y dollars. Which of the following represents the number of dollars that Peter has?
Answer/Solution
(y – x)/2
Steps/Work
To solve, we will set up two equations. Let's start by defining two variables.
A = number of dollars Peter has
B= number of dollars John has
We are given that John has x dollars more than Peter. We set up an equation:
B= x + A
We are next given that together they have a total of y dollars. We can set up our second equation:
A + B = y
Since we know that B = x + A, we can substitute x + A for B into the second equation A+ B = y.
Notice that, after the substitution, we will only have variables of A, x, and y. Thus, we have:
A + x + A = y
2A + x = y
2A = y – x
A = (y – x)/2
Answer : C
A = number of dollars Peter has
B= number of dollars John has
We are given that John has x dollars more than Peter. We set up an equation:
B= x + A
We are next given that together they have a total of y dollars. We can set up our second equation:
A + B = y
Since we know that B = x + A, we can substitute x + A for B into the second equation A+ B = y.
Notice that, after the substitution, we will only have variables of A, x, and y. Thus, we have:
A + x + A = y
2A + x = y
2A = y – x
A = (y – x)/2
Answer : C