John is 4 years older than Mary. Together they are 30. How old is Mary?: animated lesson

The problem. Here is the problem: John is 4 years older than Mary. Together they are 30. How old is Mary? Age problem with two unknown current ages (John, Mary) and two facts.

Step by step. Read the problem. Two people: John and Mary. Let a equals John prime s age now and b equals Mary prime s age now. Translate each fact into an equation. John minus Mary equals 4; John plus Mary equals 30. Write both equations in standard form. 1a minus 1b equals 4 and 1a plus 1b equals 30. Solve the system (elimination / Cramer prime s rule). Determinant equals 1 times 1 minus negative 1 times 1 equals 2. a equals (4 times 1 minus negative 1 times 30) / 2 equals 17, b equals (1 times 30 minus 4 times 1) / 2 equals 13.

The answer. So the answer is John is 17 and Mary is 13 years old. Each sentence becomes one linear equation in the two current ages; two independent equations fix both ages.

Check. John minus Mary equals 4: 4 equals 4, which checks out. John plus Mary equals 30: 30 equals 30, which checks out.