name 6 consecutive multiples of 5 which, when added together, make a sum between 340 and 350
let the first multiple of 5 be x
then the next 5 consecutive multiples of 5 are x+5, x+10, x+15, x+20, and x+25
their sum is 6x+75
then
340 ≤ 6x+75 ≤ 350 , subtract 75 from each part
265 ≤ 6x ≤ 275 , divide each part by 6
44.16 ≤ x ≤ 45.8
so the only multiple of 5 between those two value is 45
so the numbers are 45,50,55,60, 65, and 70
Let's solve this step-by-step:
Step 1: Find the lowest multiple of 5 within the given range (340 to 350).
To find the lowest multiple of 5 within the given range, we need to divide the lower bound (340) by 5 and round it up to the nearest whole number.
340 ÷ 5 = 68
Step 2: Find the highest multiple of 5 within the given range.
To find the highest multiple of 5 within the given range, we need to divide the upper bound (350) by 5 and round it down to the nearest whole number.
350 ÷ 5 = 70
Step 3: Determine the number of consecutive multiples of 5 within the given range.
To find the number of consecutive multiples of 5 within the given range, subtract the lowest multiple from the highest multiple and add 1.
70 - 68 + 1 = 3
Step 4: List the consecutive multiples of 5 within the given range.
The list of consecutive multiples of 5 within the given range (340 to 350) is:
68 x 5 = 340
69 x 5 = 345
70 x 5 = 350
So, the six consecutive multiples of 5 that make a sum between 340 and 350 are: 340, 345, and 350.
To find six consecutive multiples of 5 that add up to a sum between 340 and 350, we need to follow these steps:
Step 1: Understand the problem.
We are looking for six consecutive multiples of 5. A multiple of 5 is any number that can be evenly divided by 5, such as 5, 10, 15, etc. We want six of these multiples whose sum falls between 340 and 350.
Step 2: Determine the range.
We know that the sum falls between 340 and 350. We can narrow down the range further by considering that these six numbers are consecutive multiples of 5. The maximum sum we can get is when we add the six largest consecutive multiples of 5: 30 + 35 + 40 + 45 + 50 + 55 = 255. The minimum sum we can get is when we add the six smallest consecutive multiples of 5: 5 + 10 + 15 + 20 + 25 + 30 = 105. Therefore, our range is between 105 and 255.
Step 3: Find the six consecutive multiples.
We can start from the lowest possible sum (105) and incrementally add multiples of 5 until we fall within the desired range. Let's go through each possible group of six consecutive multiples:
a) 5 + 10 + 15 + 20 + 25 + 30 = 105
b) 10 + 15 + 20 + 25 + 30 + 35 = 135
c) 15 + 20 + 25 + 30 + 35 + 40 = 165
d) 20 + 25 + 30 + 35 + 40 + 45 = 195
e) 25 + 30 + 35 + 40 + 45 + 50 = 225
f) 30 + 35 + 40 + 45 + 50 + 55 = 255
We see that the sum of the six consecutive multiples can range from 105 to 255. Since we want the sum to be between 340 and 350, none of these combinations meet our criteria.
Step 4: Conclusion.
After checking all possibilities, we can conclude that there are no six consecutive multiples of 5 that add up to a sum between 340 and 350.
345 / 6 = 57.5
I think you can take it from there.