Answer:
Olivia is 9 years old.
Step-by-step explanation:
1/3 of o (Olivia's age) increased by 12, is twice of o minus 3. The equation for this would be 1/3o + 12 = 2o - 3. (The left side could be o/3 as well.)
1/3o + 12 = 2o - 3
Subtract 2o from both sides
-5/3o + 12 = -3
Subtract 12 from both sides
-5/3o = -3 - 12
Subtract 12 from -3 to get -15
-5/3o = -15
Multiply both sides by -3/5, the reciprocal of -5/3
o = -15 (-3/5)
Express -15(-3/5) as a single fraction
o = -15 (-3)/5
Multiply -15 by -3 to get 45
o = 45/5
Divide 45 by 5 to get 9.
o = 9
To make sure this works, substitute 9 for o.
1/3(9) + 12 = 2(9) - 3
3 + 12 = 18 - 3
15 = 15
Both sides match each other, so o equals 9.
