Answer:
Maria's present age is 7
Eduardo's present age is 5
Explanation:
- We can allow M to represent Maria's age and E to represent Eduardo's.
- We'll need a system of equations to find the two ages.
Step 1: Find first equation:
- We know that Marie is 2 years older than Eduardo.
- Thus, our first equation is M = E + 2.
Step 2: Find second equation:
- We further know that Maria was twice as old as Eduardo 3 years ago.
- Thus, the other equation we can use is M = 2E -3.
Method to solve: Substitution:
Step 3: Isolate E in first equation:
(M = E + 2) - 2
M - 2 = E
Step 4: Substitute M - 2 for E in M = 2E - 3 (our second equation) to find M:
M = 2(M - 2) -3
M = 2M - 4 - 3
M = 2M - 7
-M = -7
M = 7
Step 5: Plug in 7 for M in M = E + 2 (our first equation) to find E:
7 = E + 2
5 = E
Thus, Maria's is 7 years old while Eduardo is 5 years old.
Checking first statement: Since Maria is 7 years old and Eduardo is 5 years old, she is indeed 2 years older than Eduardo.
Checking second statement: Three years ago, Maria was 4 as 7 - 3 = 4. Three years ago, Eduardo was2 since 5 - 3 is 2. Because 4 is twice 2, Maria was indeed twice as old as Eduardo three years ago.