How many pens?
A shop sells pens for 75p each and pencils for 45p each. Noah buys a total of 12 items, spending exactly £7.35. How many pens did he buy?
Word Problem
A bridge is built across a river. One quarter of the bridge is over the left bank of the river and one third of the bridge is over the right bank. The river is 120 m wide. How long is the bridge?
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ReplyDeleteLet pens = x
ReplyDeleteLet pencils = y
x + y = 12
75x + 45y = 735 (since £7.35 = 735p)
Divide through by 15:
5x + 3y = 49
Substitute y = 12 - x:
5x + 3(12 - x) = 49
5x + 36 - 3x = 49
2x + 36 = 49
2x = 13
x = 6.5
=> Not an integer, so there is no whole number solution.
Conclusion: With £7.35, no integer solution exists.