This post will focus more on algebra, but it will use
algebra to answer an economics question.
This type of question asks you to find out an individual’s income, if
they give you two different scenarios and a price for one of the goods. The trick to answering problems like this is
to set up the problem correctly. Once
you have set up the problem, answering is a simple exercise with algebra.
If Hellen spends all her income on Lemons & Oranges
Hellen can just afford 30 Lemons & 8 Oranges per day. She could also use her entire budget to buy 6
Lemon & 14 Oranges per day. The price of Lemon is $6.How much is Hellen's
income per day?
This problem is the classic case of two equations, two
unknowns (meaning unknown variables).
Here the two equations are the different combinations of goods that
Hellen is able to purchase. The two unknowns
are the price of oranges and the total income allocated to Hellen each
day.
First let’s set up the first scenario, where Hellen is able
to purchase 30 lemons and 8 oranges. If
we denote the price of oranges as X, and the total income received per day as
Y, we will get the following equation:
30 lemons * $6 (the price of lemons) + 8 oranges * $X (the
price of oranges) = $Y (total income received per day
Or
30*6 + 8*X = Y
The second scenario has Hellen purchasing 6 lemons and 14
oranges. This equation would look like:
6*6 + 14*X = Y
Luckily, both of these equations are already solved for Y
(income) and we know that Y = Y so we can set the first equation equal to the
second equation, which gives us:
30*6 + 8*X = 6*6 + 14*X
Or
180 + 8X = 36 + 14X
Now we can subtract 36 from both sides, and subtract 8 from
both sides to get:
144 = 6X
Now we divide both sides by 6 to get X = 24
This gives us the price of oranges which we can use to
determine what the daily income amount is.
So plugging the price of oranges into the first two equations gives us:
180+8*24 = 180+192 = 372
And
36+14*24 = 36+336 = 372
So the Hellen’s daily income given the above information is
$372.
