# Candy and boxes

We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of nine?

Result

x =  51
y =  11

#### Solution:

$\ \\ b - (k-8) \cdot \ 10 = 2 \ \\ b - (k-3) \cdot \ 8 = 6 \ \\ \ \\ b-10k = -78 \ \\ b-8k = -18 \ \\ \ \\ b = 222 \ \\ k = 30 \ \\ \ \\ b - (k-y) \cdot \ 9 = x \ \\ 222 - (30-y) \cdot \ 9 = x \ \\ x = 9n+6 \ \\ y = n+6 \ \\ n > = 2 \ \\ 9n+6 < = 222 \ \\ n< = 24 \ \\ 2< = n < = 24 \ \\ n = 5 \ \\ x = 9 \cdot \ n+6 = 9 \cdot \ 5+6 = 51$
$y = n+6 = 5+6 = 11$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 1 comment: Math student
this didnt  help me #### Following knowledge from mathematics are needed to solve this word math problem:

Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? Do you solve Diofant problems and looking for a calculator of Diofant integer equations?

## Next similar math problems:

1. CZK coins Thaddeus and Jolana together have 15 CZK. Jolana has half of Thaddeus money. Nevertheless Jolana has 3 coins and Thaddeus 2 coins. Which coin has Thaddeus and Jolana (Help: CZK coins has values 1,2,5,10,20,50 CZK)?
2. Mistake Nicol mistake when calculate in school. Instead of add number 20 subtract it. What is the difference between the result and the right result?
3. Unknown x If we add to unknown number 21, then divide by 6 and then subtract 51, we get back an unknown number. What is this unknown number?
4. Sequence In the arithmetic sequence is a1=-1, d=4. Which member is equal to the number 203?
5. Line Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
6. Number Calculate the integer number which, divided by 34 gives 10 and the rest 25.
7. 15 number What number is smaller (greater) by 15 than its half?
8. Modulo Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 .
9. Integer Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
10. Mysterious number The magician thinks the number: "The mysterious number is first divided by minus five, dividing the result by three, multiplying the number by ten, and dividing the resulting number by minus four. This gives result 5. Can you reveal the mysterious number?
11. Four integers Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
12. Two numbers 6 Fill two natural numbers a, b: 7 + blank- blank = 5
13. Repairman Repairman has vowed to do repair work at the plant for 25 days. However work had to be shortened, and therefore he took helper worker. Together they made all the corrections for the whole days. How long it would take work to helper worker?
14. Chickens and rabbits In the yard were chickens and rabbits. Together they had 51 heads and 122 legs. How many chickens and how many rabbits was in the yard? Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 3484. Calculate how many books Ladislav could buy at the price of 48 and 52 euros if he don't want fill whole home library and he can buy only 70 books? Theo had a balance of -$4 in his savings account. After making a deposit, he has$25 in his account. What is the overall change to his account? Solve equation with negatives: X/(-5) + 2 = -9