There are a total of 15 apartments in two buildings. The difference of two times the number of apartments in the first building and three times the number of apartments in the second building is 5. Write a system of equations to model the relationship between the number of apartments in the first building and the number of apartments in the second building. How many apartments are in each building?
+33654 Let f be number of apartments in first building and s be number in second building.
Then we are told:
f + s = 15 ...(1)
2*f - 3*s = 5 ...(2)
From (1) we can write f = 15 - s
Replace f in (2) by 15 - s to get:
2*(15 - s) - 3s = 5
30 - 2s - 3s = 5
30 - 5s = 5
Subtract 5 from both sides
25 - 5s = 0
Add 5s to both sides
25 = 5s
Divide both sides by 5
s = 5
Put this back into (1)
f + 5 = 15
Subtract 5 from both sides
f = 10
+33654 Let f be number of apartments in first building and s be number in second building.
Then we are told:
f + s = 15 ...(1)
2*f - 3*s = 5 ...(2)
From (1) we can write f = 15 - s
Replace f in (2) by 15 - s to get:
2*(15 - s) - 3s = 5
30 - 2s - 3s = 5
30 - 5s = 5
Subtract 5 from both sides
25 - 5s = 0
Add 5s to both sides
25 = 5s
Divide both sides by 5
s = 5
Put this back into (1)
f + 5 = 15
Subtract 5 from both sides
f = 10
