Expert: Josh - 11/1/2006

Question
Can you tell me what this problem would be called? My son doesn't know and I want to get him help online.
1.4f = 0.0882

f =  

Answer
Hi Andrew,

You are exactly right. This problem introduces the basic concept of algebra. The idea here, is to work out the value of "f" (this is called a "variable", or "place-holder", if you like, it represents the "unknown") from the equation "1.4*f=0.0882".

We obtain the answer dividing both sides by 1.4. This gives f=0.0882/1.4. (You can use a calculator if you wish to simplify this numerically) It reduces to f=0.063

In general, we usually have one or more unknown quantities that we need to determine. Invariably, the problem is translated into a system of equations. By putting pieces of information together, we use standard algebraic techniques (combination of addition, subtraction and multiplication between equations) to eliminate the unknowns down to a single variable. Once the value of an unknown quantitity is determined, we work our way back, substituting known values in expressions, exploiting the relationship between different variables.

e.g., Suppose Kate and Allison went to an icecream shop. Kate ordered a strawberry flavored icecream and Allison ordered a chocolate-flavored icecream. They paid $5.70. Kate's elder brother, Aaron, took a bite of each and he really liked the chocolate flavor. He went back to the shop to get two chocolate ice-cream for himself and a strawberry icecream for his gf. He paid $8.40. How much did the strawberry and chocolate icecream costed?

Solving this problem. Let "s" and "c" represent the cost of a strawberry and chocolate icecream, respectively.

In the first instance, for Kate and Allison, we can extract the key words "1 strawberry"..."1 chocolate"..."cost $5.70" and translate this into a mathematical equation as s+c=5.70.

In the second instance, we can extract the key words "2 chocolate", "1 strawberry", "cost $8.40" and translate this into a mathematical equation as s+2c=8.40.

Observe that we have two equations and two unknowns ("s" and "c"). Our task is to find values of "s" and "c" (cost of strawberry and chocolate) which satisfy the conditions s+c=5.7 and s+2c=8.4 simultaneously.

s+c=5.7 ...[#1]
s+2c=8.4...[#2]

We can do this in various ways. Here, we can rearrange the first equation [#1] as s=5.7-c. Let's call this [#3].

Putting [#3] into the second equation [#2], we get (5.7-c)+2c=8.4. This process eliminates one of the unknown, leaving us with 5.7+c=8.4, which simplifies to c=8.4-5.7=2.7. i.e., cost of chocolate is $2.70. Now, putting this (now known value of "c") back into equation [#3], we get s=5.7-2.7=3. So, the cost of strawberry is $3.00.

Algebra in high school normally involves solving problems like this. I hope you find this useful.

Cheers:)

P.S. I would describe your original problem as "solving an equation with one unknown". In my example, we had two equations and two unknowns.