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Question 328686: Ann needs 6 pens and 14 books costing a total of Sh. 310. Agnes, Annes sister needs 12 similar pens and 10 similar books which cost a total of Sh. 314. How much should their mother have to buy all the books?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Ann needs 6 pens and 14 books costing a total of Sh. 310.
Agnes needs 12 pens and 10 books which cost a total of Sh. 314.
Apparently the pens cost the same each and the books cost the same each.
You have 2 equations that need to be solved simultaneously
Let p = price of each pen
Let b = price of each book
Your equations are:
6p + 14b = 310
12p + 10b = 314
If we multiply both sides of the first equation by 2, then we can cancel out the p and solve for b. multiplying both sides of any equation by the same number does not change the equality. If it was equal before, it will be equal after.
Multiply both sides of the first equation to get:
12p + 28b = 620
subtract the second equation from that to get:
12p + 28b = 620
minus:
12p + 10b = 314
equals:
0p + 18b = 306
which is equivalent to:
18b = 306
divide both sides of this equation by 18 to get:
b = 17
the price of each book is Sh. 17.
Since you know that each book costs Sh. 17, you can solve for the price of each pen by substituting in one of the original equations.
Take 6p + 14b = 310
When b = 17, this equation becomes:
6p + 238 = 310
subtract 238 from both sides of this equation to get:
6p = 72
divide both sides of this equation by 6 to get:
p = 12
the price of each pen is Sh. 12 and the price of each book is Sh. 17.
From your original equations, you can see that:
6p + 14b = 310
12p + 10b = 314
gets you a total of:
18 pens and 24 books for a total of Sh. 624.
multiply the number of pens by the price of each pen and the number of each book by the price of each book to get:
18 * 12 = 216 total cost for pens
24 * 17 = 408 total cost for books
total spent is 216 + 408 = 624 which agrees with the total you got just above.
Your answer is that the amount of money spent on books is equal to Sh. 408
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