ms. mckee wants to give each student in her class some candy. She wants everyone to recieve an equal number of jelly beans. She
has less than 100 jellybeans. If she makes groups of 2,3, or 4 she will have 1 jelly bean left over. If she makes groups of 5, she will have no jellybeans left over, How many jellybeans could she have?
Ok so since she makes groups of 5 an no left over, the number is divisble by 5 means that it ends with 5 or 0 possible ones are 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95
groups of 2, will have 1 jelly bean left over it is not divisble by 2, means it doesn't end with 0 (ending with 0 means it is divisible by 10, and 10 is divisible by 2) 5,15,25,35,45,55,65,75,85,95
groups of 3 not divisble by 3 (a hack to test, is that you add the digits and if the sum is divisble by 3, then the number is divisble), the list below is eliminated numbers divisble by 3
5,25,35,55,65,85,95 if makes group of 2 will have exactly 1 left over 5/3 has remainder of 2, eliminate 25 works so far (2*12=24,3*8=24,4*6=24) 35/4 has remainder of 3, eliminate 55/4 has remainder of 3, eliminate 65/3 has remainder of 2, eliminate 85 works 95/3 has remainder of 2,eliminate
So we are told that if the teacher makes the number of jelly beans she has (call that x) into groups of 2, 3, or 4 she'll have 1 jelly left over. to put that in math terms, x leaves a remainder of 1 when divided by 2, 3, or 4. This then implies that (x-1) is a multiple of 2, 3, or 4 (think about it!!!). all common multiples of 2, 3, or 4 must be a multiple of the LEAST common multiple of 2, 3 and 4. the least common multiple of those 3 numbers is 12. this means our common multiples can be: 12, 24, 36, 48, 60, 72, 84, 96 (we stop listing here because the number of jelly beans is less than 100) this also means the possible number of jelly beans she can have is the numbers in the previous list plus 1 (remember it is x-1 NOT x that is the common multiple of 2, 3, 4): 13, 25, 37, 49, 61, 73, 85, 97 now we use our last clue which is if the teacher groups her jelly beans in groups of 5 there will be none left over. this is equivalent to saying that the number of jelly beans is a multiple of 5. we look through our 2nd list and find that only 25, and 85 is a multiple of 5. therefore the number of jelly beans the teacher can have is 25 and 85. note that we took the problem in steps and used process of elimination to determine which of the natural numbers less than 100 can be the answer to the question. this is a very very good strategy in problem solving, but it can be challenging to know what order to take the "steps" but that can be mastered with patient practice.
The triangular prism shown has 2 triangular face(s) and 3 lateral face(s).
The area of one triangular face is 7.5 mm²
The surface area of the triangular prism is 135 mm²
Step-by-step explanation:
A triangular face of the prism is the face that has a three sided figure while the lateral faces are faces with four-sided figure. As seen from the triangular prism, it has 2 triangular faces since it is made up of 2 right angled triangles and has 3 lateral faces since it is made up of 3 rectangles which are 4 sided each.
Area of one triangular face =
Given base = 2.5 mm and height = 6 mm
Area of one triangular face =
Surface area of triangular prism = bh + pH
b= base of the triangle = 2.5 mm
h- height of the triangle = 6 mm
p= perimeter of the triangle = base + height + slant height = 2.5+6+6.5
that leaves $0.20 for other coins (dimes / pennies)
Step-by-step explanation:
First, suppose she has only quarters and nickels and no other coins. Then if C is the identical number of coins of each type, then 5C + 25C = 320, so 30C = 320 and 3C = 32, but there is no integer solution to this. So she must have at least one other type of coin.
Assume she has only quarters, nickels, and dimes. Then if D is the number of dimes, 5C + 25C + 10D = 320, which means 30C + 10D = 320, or 3C + D = 32. The smallest D can be is 2, leaving 3C = 30 and thus C = 10. So in this scenario she would have 10 quarters, 10 nickels, and two dimes to make $2.50 + $0.50 + $0.20 = $3.20.
This has to be the highest number, because if she had 11 quarters and 11 nickels, that alone would add up to 11(0.25) + 11(0.05) = $3.30, which would already be too much.
