Algebraaaa?

Question

Mario's age is 2 years more than twice Nadia's age. In 9 years her age will be 2/3 of his. How old is Mario and Nadia?


Hey guys.. i have a million of these flippin word problems! could you help me understand the rest by using this one as an example. just walk me through on how you got the answer.. thank you so much!!

Answer 1

Let Mario's age = m, and Nadia's age = n.

Step 1: Write each statement as an equation:
Mario's age is 2 years more than twice Nadia's age.
m = 2 + 2n
In 9 years her age will be 2/3 of his.
2/3(m + 9) = n + 9

Step 2: Substitute one equation for another.
In this case, use the first equation to subsitute for m.
2/3(m + 9) = n + 9
2/3((2 + 2n) + 9) = n + 9
2/3(2n + 11) = n + 9
4/3n + 22/3 = n + 9
4/3n - n = 9 - 22/3
1/3n = 27/3 - 22/3 = 5/3
3 * 1/3n = 3 * 5/3
n = 5

Now, substitute n back into the first equation:
m = 2n + 2
m = 2(5) + 2 = 10 + 2 = 12.

Check: Use both values in the second equation:
2/3(m + 9) = n + 9
2/3(12 + 9) = 5 + 9
2/3(21) = 14
14 = 14