Janson bought 7 identical pens and had $4.20 left. He could have bought 10 pens with all his money. How much did Janson have?
$4.20 is 3/10 of what he had ... (10 - 7) / 10
$4.20 / .3 = ?
Let Y = cost of each pen
10Y = 7Y + 4.20
3Y = 4.20
Y = 1.40 = cost of each pen; therefore,
10 pens@ 1.40 each = $14.00 is how much money Ben had initially.
To find out how much money Janson had, we need to use algebra and solve the problem step by step.
Let's assume the cost of each pen is 'x' dollars.
According to the given information, Janson bought 7 identical pens, so he spent a total of 7x dollars.
We also know that he had $4.20 left after the purchase. This means that the total amount of money Janson had initially was the money he spent (7x dollars) plus the money he had left ($4.20).
So, we can set up the following equation:
7x + $4.20 = total amount of money Janson had.
Now, we are given another piece of information: if Janson bought 10 pens with all his money, it means that the total cost of 10 pens should be equal to the total amount of money he had.
Therefore, we can set up another equation:
10x = total amount of money Janson had.
Since we know that both equations represent the same total amount of money Janson had, we can equate them:
7x + $4.20 = 10x.
Now, we can solve this equation to find the value of 'x', which will tell us the cost of each pen.
Subtracting 7x from both sides, we get:
$4.20 = 3x.
Dividing both sides by 3, we find:
x = $4.20 / 3.
Evaluating this expression, we get:
x = $1.40.
So, each pen costs $1.40.
To find out how much money Janson had, we substitute the value of 'x' into either of the two equations we set up earlier.
Let's use the equation 7x + $4.20 = total amount of money Janson had.
Substituting x = $1.40, we get:
7($1.40) + $4.20 = total amount of money Janson had.
Simplifying this expression, we get:
$9.80 + $4.20 = total amount of money Janson had.
Combining like terms, we find:
$14 = total amount of money Janson had.
Therefore, Janson initially had $14.