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Jlenok [28]
3 years ago
12

How many pennies could you have if: When you Break de Pennies into groups of 2, you have 1 penny left over, AND when you break t

he pennies into groups of 3, and you have 1 penny left over, AND when you break the pennies into groups of 5, you have 1 penny left?
Mathematics
1 answer:
MariettaO [177]3 years ago
6 0

Answer:

The answer is 31 pennies

Step-by-step explanation:

we have to find a number that gives a remainder of 1 when divided by both 2, 3 and 5.

The easiest way to do this is to list the factors of 5, add 1 to it, and test them until we find the one with a remainder of 1 by all three divisors. This is done as follows:

1) factor: 5 (+1) = 6

6 ÷ 2 = 3 remainder 0

6 ÷ 3 = 2 remainder 0

since there is a remainder of 0, when divided by 3, 6 is wrong

2) factor; 10 (+1) = 11

11 ÷ 3 = 3 remainder 2 ( 11 is not the correct answer

3) factor : 15 (+1) = 16

16 ÷ 2 = 8 remainder 0 ( 16 is  not the correct answer

4) factor : 20(+1) = 21

21 ÷ 3 = 7 remainder 0 ( 21 is wrong)

5) factor : 25(+1) = 26

26 ÷ 2 = 13 remainder 0 ( 26 is wrong)

6) factor : 30(+1) = 31

31 ÷ 2 = 15 Remainder 1

31 ÷ 3 = 10 Remainder 1

31 ÷ 5 = 6 Remainder 1

since all three divisors give a remainder of 1, the correct answer is 31

Therefore you have 31 pwnnies

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Answer: It has one solution. The solution is (x,y) = (-4,-3)

Add up the equations doing so straight down

x + -x = 0x = 0 so the x terms go away

2y + 2y = 4y

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We end up with 4y = -12 so y = -3 after you divide both sides by 4. Use this y value to find the value of x

x+2y = -10

x + 2(-3) = -10

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x = -4

The single solution is (x,y) = (-4,-3)

As a check, plug this solution into each equation to see if you get a true statement or not. Let's do so with the first equation

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-10 = -10 .... true

and then the second equation

-x+2y = -2

-(-4) + 2(-3) = -2

4 - 6 = -2

-2 = -2 .... true

both equations are true, so the solution is confirmed

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3 years ago
when the sum of an unknown number z and twenty two is divided by the same unknown number,the quotient is twelve what is the unkn
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You said that quotient is 12.              (z + 22) / z  =  12

Multiply each side by 'z' :                  (z + 22)       =  12 z

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