One-third of Olivia's age, increased by 12, is equal to twice her age, decreased by 3. How old is Olivia?

Olivia is 9 years old

Twice her age decreased by 3 is expressed as 2x - 3

Equate both expressions and find x

1/3x + 12 = 2x - 3

1/3x - 2x = -3-12

(x-6x)/3 = -15

-5x = -45

x = 9

Hence Olivia is 9 years old

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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.

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

step-by-step explanation: