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If twice the present age of Pedro is decreased from Petra's age 5 years ago, the result is 4. Nine times Pedro's age 3 years ago exceeds 4 times Petra's present age by 4. WHat were their ages last year?

Guest Nov 14, 2015

#1**+5 **

If twice the present age of Pedro is decreased from Petra's age 5 years ago, the result is 4. Nine times Pedro's age 3 years ago exceeds 4 times Petra's present age by 4. WHat were their ages last year?

Let pedro's age today be P

Let Petra's age today be T

2P - (T - 5)=4

9 (P-3) - 4T=4

Solve the following system:

{5+2 P-T = 4 | (equation 1)

9 (P-3)-4 T = 4 | (equation 2)

Express the system in standard form:

{2 P-T = -1 | (equation 1)

9 P-4 T = 31 | (equation 2)

Swap equation 1 with equation 2:

{9 P-4 T = 31 | (equation 1)

2 P-T = -1 | (equation 2)

Subtract 2/9 × (equation 1) from equation 2:

{9 P-4 T = 31 | (equation 1)

0 P-T/9 = (-71)/9 | (equation 2)

Multiply equation 2 by -9:

{9 P-4 T = 31 | (equation 1)

0 P+T = 71 | (equation 2)

Add 4 × (equation 2) to equation 1:

{9 P+0 T = 315 | (equation 1)

0 P+T = 71 | (equation 2)

Divide equation 1 by 9:

{P+0 T = 35 | (equation 1)

0 P+T = 71 | (equation 2)

Collect results:

Answer: |

| {P = 35 Pedro's age today

T = 71 Petra's age today

Guest Nov 15, 2015

#2**+6 **

Best Answer

Their ages LAST YEAR would, of course, be 1 year less:

71 -1=70 Petra's age

35 - 1=34 Pedro's age.

Guest Nov 15, 2015