leroy gave each of his four children the same amount of money. one spent all but

Question

leroy gave each of his four children the same amount of money. one spent all but 13 cents on 5 cent candy bars. the second spent all but 3 cents on 6 cent popsicles. the third spent all but 2 cents on 11 cent comic books. the fourth bought a $3 game, but didn't have enough money to buy another. how much money did each child get?

I tr to set up the congruence but I'm not sure if it is right:

5x=13(mod4), 6x=3(mod4), 11x=2(mod4), 300x=0(mod4).

Please explain how you set up your congruence and why you think it's the correct one?

Explanation / Answer

Let x cents be the amount given to each of the children.

Then x = 5t + 13 (t candy bars purchased say,left over amount = 13)

This gives x = 13 (mod 5)

similarly the second and third children information gives us

x = 3 (mod 6)   (left over amount is 3 cents when he spent in multiples of 6)

x = 2 (mod 11)

Finally the last piece of information gives us

300 <= x < 600 (he has money to buy 1 game but dint have enough money to buy second)

So we have to find a solution to the set of congruence equations

x = 13 (mod 5)

x = 3 (mod 6)

x = 2 (mod 11)

subject to x lies in [300,600)

The congruence set has x = 123 as a solution.

So general solution is 123 + k*lcm(5,6,11) = 123 + 330k

123 + 330k lies in [300,600) for k = 1

Hence the money that each child got = 123+330 = 453

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.