James has a certain amount of money. If he buys $3$ pens and $2$ pencils, he will have $\$2$ left over. If he buys $2$ pens and
1 answer:
The cost of pen and pencils are related to the number that can be bought
with a given amount of money.
- <u />
<u />
Reasons:
The given parameters are;
If the number number of pens and pencils James buys = 3 pens and 2 pencils, the amount James will have left = $2
If the number of pens and pencils James buys = 2 pens and 3 pencils, the amount James will have left = $6
The amount of money Judith has = The amount of money with James
The number of pens and pencil James and Judith can buy = 6 pens and 6 pencils
The cost of one pen = a
The cost of one pencil = b
Required:
To find the ordered pair (a, b)
Solution:
Let <em>X</em> represent the initial amount of money James has, we get;
X - (3·a + 2·b) = 2...(1)
X - (2·a + 3·b) = 6...(2)
2·X = 6·a + 6·b...(3)
Therefore;
X = (6·a + 6·b) ÷ 2 = 3·a + 3·b
Which from equation (1) gives;
3·a + 3·b - (3·a + 2·b) = 2
3·a + 3·b - 3·a - 2·b = 2
3·b - 2·b = 2
b = 2
Subtracting equation (1) from equation (2) gives;
(X - (2·a + 3·b)) - (X - (3·a + 2·b)) = 6 - 2 = 4
-2·a - 3·b + 3·a + 2·b = 4
a - b = 4
a = 4 + b
∴ a = 4 + 2 = 6
a = 6
<u />
<u />
<u />
Learn more about word problems and simultaneous equations here:
You might be interested in