Problema Solution
Serena and Tyler are wrapping gift boxes at the same pace. Serena starts first, as shown in the diagram. (2 boxes wrapped). Write an algebraic expression that represents the number of boxes Tyler will have wrapped when Serena has wrapped x boxes. 2nd diagram: Serena 3 boxes Tyler 1. 3rd diagram: Serena 4 boxes Tyler 2 boxes.
Answer provided by our tutors
let y represent the number of boxes that Tyler has wrapped
and we will assume that the algebraic expression is: y = ax + b, where a and b are constants
we know that for x = 2, y =0 thus
2a + b = 0
for x = 3, y = 1
3a + b = 1
for x = 4, y = 2
4a + b = 2
by solving the system of equations
2a + b = 0
3a + b = 1
we find
a = 1
b = -2
click here to see the step by step solution of the system of equations
y = x - 2
indeed for x = 4 we have y = 4 - 2 or y = 2
an algebraic expression that represents the number of boxes Tyler will have wrapped when Serena has wrapped x boxes is:
y = x - 2.