Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
The cost of pen and pencils are related to the number that can be bought
with a given amount of money.
- [tex]\underline{The \ ordered \ pair \ (a, \, b) \ is \ (6, \, 2)}[/tex]
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 X 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
[tex]\underline{The \ ordered \ pair \ (a, \, b) \ is \ (6, \, 2)}[/tex]
Learn more about word problems and simultaneous equations here:
https://brainly.com/question/14294864
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
