Solve the following word problem using two variables. show each step of your work. juan is three years older than maria. the sum of their ages is 21. find both ages.

To solve this problem, we can use a system of equations. Let’s let the variable j represent Juan’s age and the variable m represent Maria’s age.

From our given information, we can construct two equations with our given variables:

j + m = 21

m + 3 = j

To solve, we can manipulate our second equation to be for m in terms of j.

m + 3 = j

m = j - 3

Now, we can substitute in this value for m into our first equation.

j + m = 21

j + (j -3) = 21

Next, we can add the variable terms on the left side of the equation.

2j -3 = 21

Next, we can add 3 to both sides to get the variable term alone on the left side of the equation.

2j = 24

Finally, we should divide both sides by 2 in order to solve for j.

j = 12

Finally, we must substitute this value for j into one of the original equations.

j + m = 21

12 + m = 21

m = 9

Therefore, Maria is 9 and Juan is 12.

Hope this helps!

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