The sum of three positive integers is 42. The smallest integer is five less than the middle integer. The middle integer is two less than the greatest integer. Define a variable, write an equation and solve to find the three integers.
+307 Let the three integers be x, y and z, from smallest to largest. A system of equations composed from the information given would look like this:
x+y+z=42
x+5=y
y+2=z
Substitution finds that z= (x+5)+2=x+7, and so x+(x+5)+(x+7)=42.
3x+12=42
3x=30
x=10
y=15
z=17
+307 Let the three integers be x, y and z, from smallest to largest. A system of equations composed from the information given would look like this:
x+y+z=42
x+5=y
y+2=z
Substitution finds that z= (x+5)+2=x+7, and so x+(x+5)+(x+7)=42.
3x+12=42
3x=30
x=10
y=15
z=17
