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A baker has between 40 and 60 cookies. If he packs them 6 to a box, there are 5 left over, but if he packs them 7 to a box, there are 4 left over. How many cookies are in the baker’s supply?

Explanation	Calculations	Help
$We name the number of cookies n and translate the condition "If he packs them 6 to a box, there are 5 left over" .$	$n = number of cookies n = 6 k + 5$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We introduce m as the number of full boxes when packing cookies 7 per box and translate the condition "if he packs them 7 to a box, there are 4 left over" .$	$n = 7 m + 4$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We list all values between 40 and 60 that satisfy the first condition.$	$n = 6 k + 5 n = 41, 47, 53, and 59$
$We test 41 in the second condition and rule it out because it leaves a remainder of 6 instead of 4.$	$41 = 7 \times 5 + 6$
$We test 47 in the second condition and rule it out because it leaves a remainder of 5 instead of 4.$	$47 = 7 \times 6 + 5$
$We test 53 and confirm it leaves the correct remainder of 4, so it satisfies both conditions.$	$53 = 7 \times 7 + 4$

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D

A baker has between 40 and 60 cookies. If he packs them 6 to a box, there are 5 left over, but if he packs them 7 to a box, there are 4 left over. How many cookies are in the baker’s supply?

Explanation	Calculations	Help
$We name the number of cookies n and translate the condition "If he packs them 6 to a box, there are 5 left over" .$	$n = number of cookies n = 6 k + 5$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We introduce m as the number of full boxes when packing cookies 7 per box and translate the condition "if he packs them 7 to a box, there are 4 left over" .$	$n = 7 m + 4$	Theory & Tactics Method Card TRANS5-F Click to view full details
$We list all values between 40 and 60 that satisfy the first condition.$	$n = 6 k + 5 n = 41, 47, 53, and 59$
$We test 41 in the second condition and rule it out because it leaves a remainder of 6 instead of 4.$	$41 = 7 \times 5 + 6$
$We test 47 in the second condition and rule it out because it leaves a remainder of 5 instead of 4.$	$47 = 7 \times 6 + 5$
$We test 53 and confirm it leaves the correct remainder of 4, so it satisfies both conditions.$	$53 = 7 \times 7 + 4$

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D