Word problems
"Age" Word Problems (page 1 of 2)
In January of the year 2000, I was one more than eleven times as old as my son William. In January of 2009, I was seven more than three times as old as him. How old was my son in January of 2000?
Obviously, in "real life" you'd have walked up to my kid and and asked him how old he was, and he'd have proudly held up three grubby fingers, but that won't help you on your homework. Here's how you'd figure out his age for class:
First, name things and translate the English into math: Let "E " stand for my age in 2000, and let "W " stand for William's age. Then E = 11W + 1 in the year 2000 (from "eleven times as much, plus another one"). In the year 2009 (nine years after the year 2000), William and I will each be nine years older, so our ages will be E + 9 and W + 9. Also, I was seven more than three times as old as William was, so E + 9 = 3(W + 9) + 7 = 3W + 27 + 7 = 3W + 34. This gives you two equations, each having two variables:
E = 11W + 1
E + 9 = 3W + 34
If you know how to solve systems of equations, you can proceed with those techniques. Otherwise, you can use the first equation to simplify the second: since E = 11W + 1, plug "11W + 1 " in for "E " in the second equation:
E + 9 = 3W + 34
(11W + 1) + 9 = 3W + 34
11W – 3W = 34 – 9 – 1
8W = 24
W = 3
Remember that the problem did not ask for the value of the variable W; it asked for the age of a person. So the answer is: William was three years old in January of 2000.
The important steps above were to set up the variables, labelling them all clearly with their definitions, and then to increment the variables by the required amount (in this case, by 9) to reflect the passage of time. Don't try to use the same expression to stand for two different things. If "E " stands for my age in 2000, then "E " can not also stand for my age in 2009. Make sure that you are very explicit about this when you set up your equations; write down the two sets of information (our
In January of the year 2000, I was one more than eleven times as old as my son William. In January of 2009, I was seven more than three times as old as him. How old was my son in January of 2000?
Obviously, in "real life" you'd have walked up to my kid and and asked him how old he was, and he'd have proudly held up three grubby fingers, but that won't help you on your homework. Here's how you'd figure out his age for class:
First, name things and translate the English into math: Let "E " stand for my age in 2000, and let "W " stand for William's age. Then E = 11W + 1 in the year 2000 (from "eleven times as much, plus another one"). In the year 2009 (nine years after the year 2000), William and I will each be nine years older, so our ages will be E + 9 and W + 9. Also, I was seven more than three times as old as William was, so E + 9 = 3(W + 9) + 7 = 3W + 27 + 7 = 3W + 34. This gives you two equations, each having two variables:
E = 11W + 1
E + 9 = 3W + 34
If you know how to solve systems of equations, you can proceed with those techniques. Otherwise, you can use the first equation to simplify the second: since E = 11W + 1, plug "11W + 1 " in for "E " in the second equation:
E + 9 = 3W + 34
(11W + 1) + 9 = 3W + 34
11W – 3W = 34 – 9 – 1
8W = 24
W = 3
Remember that the problem did not ask for the value of the variable W; it asked for the age of a person. So the answer is: William was three years old in January of 2000.
The important steps above were to set up the variables, labelling them all clearly with their definitions, and then to increment the variables by the required amount (in this case, by 9) to reflect the passage of time. Don't try to use the same expression to stand for two different things. If "E " stands for my age in 2000, then "E " can not also stand for my age in 2009. Make sure that you are very explicit about this when you set up your equations; write down the two sets of information (our