Word Problems
Examples of Age word problems :
1. Six years ago Jun was 4 times as old as Joan.In four years, he would be twice as old as Joan. How old are they now?
6 years ago joan x jun 4x
..
after 4 years joan x+10
Jun 4x+10
4x+10=2(x+10)
4x+10=2x+20
4x-2x=20-10
2x=10 x=5 joan 6 years ago. Now age = 11
Jun 4x, = 20, 6 years ago. Now age =26 years now
2. At present, Pedro's age is 25percent of his father's age.Twenty years from now Pedro's age would be 50percent of his fathers age. How old are they?
Let pedro's age be x ( pedro's age is 1/4 of father'e age OR father is 4 times pedros age) father's age = 4x
..
20 years later pedro = x+20
Father = 4x+20
2(x+20)=4x+20
2x+40 =4x+20
2x=20
x=10 pedro's age now father= 10*4 = 40 years
3. Kevin is 4 years older than Margaret.
Next year Kevin will be 2 times as old as Margaret.
How old is Kevin?
Kevin x
Margaret x-4
(X+1)(X-4+1=x-3),x+1=2*(x-3),x+1=2x-6
1+6=2x-x
7=x
4. Ann is 2 years older than Betty.
Last year Ann was 2 times as old as Betty.
How old is Ann?
Ann x
Betty x-2 x-1=2*(x-3) x-1=2x-6
6-1=2x-x
5=x
5. Mark is 3 years older than Philip. Two years ago Susan was twice as old as Tom.
Find their present ages.
Philip x
Mark 2x x+2=2x+2-3 x+2=2x-1
2+1=2x-x
3=x
Mixture word problems:
1.A store owner wants to mix cashews and almonds. Cashews cost 2 dollars per pound and almonds cost 5 dollars per pound. He plans to sell 150 pounds of a mixture. How many pounds of each type of nuts should be mixed if the mixture will cost 3 dollars?
Solution #1: Use of one variable leading to a linear equation
Let x be the number of pounds of cashews
So, 150 - x will represent the number of almonds
Since each pound of the mixture cost 3 dollars, 150 pounds will cost 3 × 150 = 450 dollars
Cost of cashews + cost of almonds = 450
2 × x + (150 - x) × 5 = 450
2x + 150 × 5 - x × 5 = 450
2x + 750 - 5x = 450
2x - 5x + 750 = 450
-3x + 750 = 450
-3x + 750 - 750 = 450
1. Six years ago Jun was 4 times as old as Joan.In four years, he would be twice as old as Joan. How old are they now?
6 years ago joan x jun 4x
..
after 4 years joan x+10
Jun 4x+10
4x+10=2(x+10)
4x+10=2x+20
4x-2x=20-10
2x=10 x=5 joan 6 years ago. Now age = 11
Jun 4x, = 20, 6 years ago. Now age =26 years now
2. At present, Pedro's age is 25percent of his father's age.Twenty years from now Pedro's age would be 50percent of his fathers age. How old are they?
Let pedro's age be x ( pedro's age is 1/4 of father'e age OR father is 4 times pedros age) father's age = 4x
..
20 years later pedro = x+20
Father = 4x+20
2(x+20)=4x+20
2x+40 =4x+20
2x=20
x=10 pedro's age now father= 10*4 = 40 years
3. Kevin is 4 years older than Margaret.
Next year Kevin will be 2 times as old as Margaret.
How old is Kevin?
Kevin x
Margaret x-4
(X+1)(X-4+1=x-3),x+1=2*(x-3),x+1=2x-6
1+6=2x-x
7=x
4. Ann is 2 years older than Betty.
Last year Ann was 2 times as old as Betty.
How old is Ann?
Ann x
Betty x-2 x-1=2*(x-3) x-1=2x-6
6-1=2x-x
5=x
5. Mark is 3 years older than Philip. Two years ago Susan was twice as old as Tom.
Find their present ages.
Philip x
Mark 2x x+2=2x+2-3 x+2=2x-1
2+1=2x-x
3=x
Mixture word problems:
1.A store owner wants to mix cashews and almonds. Cashews cost 2 dollars per pound and almonds cost 5 dollars per pound. He plans to sell 150 pounds of a mixture. How many pounds of each type of nuts should be mixed if the mixture will cost 3 dollars?
Solution #1: Use of one variable leading to a linear equation
Let x be the number of pounds of cashews
So, 150 - x will represent the number of almonds
Since each pound of the mixture cost 3 dollars, 150 pounds will cost 3 × 150 = 450 dollars
Cost of cashews + cost of almonds = 450
2 × x + (150 - x) × 5 = 450
2x + 150 × 5 - x × 5 = 450
2x + 750 - 5x = 450
2x - 5x + 750 = 450
-3x + 750 = 450
-3x + 750 - 750 = 450