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Paula, dianna and annie are three friends. paula is twice as old as dianna, and in 2 years she will be three times as old as annie. if dianna is 5 years older than annie, how old is paula?

Respuesta :

chrisaprilep3t169
make x = Paula, y = Dianna, and z = Annie

The 3 equations to set up and solve for are:

x = 2y
x + 2 = 3(z +2)
y = z + 5

Rewriting and reducing the equations as:  

x = 2y => y = x/2
x + 2 = 3(z +2) => x + 2 = 3z + 6 => x - 4 = 3z
y = z + 5 

Then solving for x (Paula's age) gives:
x+2 = 3(z-5+2) = 3(x/2 - 3) 
x+2 = 3/2 x - 9 
x/2 = 11 
x = 22

abidemiokin

Paula is 22 years old

Simultaneous equation

  • Let the age of Anni be "x"

If Dianna is 5 years older than annie, the age of dianna will be

x + 5

If Paula is twice as old as Dianna, then the age Paula will be 2(x+5)

The three rquired equation will be:

x = 2y

x + 2 = 3(z +2)

y = z + 5

Rewriting and reducing the equations as:  

From 3, z = y - 5 ...... 4

Substitute 1 and 4 into (2)

2y + 2 = 3(y - 5 + 2)

2y + 2 = 3y - 9

-y = -9 - 2

y = 11

Since x = 2y

x = 2(11)

x = 22

Hence Paula is 22 years old

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