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Answer :
Sure, let's go through each question step-by-step:
1. What day of the week will it be 75 days from today if today is Wednesday?
- Today is Wednesday.
- There are 7 days in a week.
- To find out what day of the week it will be in 75 days, calculate the remainder of 75 divided by 7 (75 % 7).
- 75 divided by 7 gives a remainder of 5.
- Moving 5 days forward from Wednesday:
- Wednesday -> Thursday (1),
- Thursday -> Friday (2),
- Friday -> Saturday (3),
- Saturday -> Sunday (4),
- Sunday -> Monday (5).
- So, in 75 days, it will be Monday.
2. If thrice a number decreased by 10 equals 53, find the number.
- Let the number be [tex]\( x \)[/tex].
- The equation is: [tex]\( 3x - 10 = 53 \)[/tex].
- Add 10 to both sides to get: [tex]\( 3x = 63 \)[/tex].
- Divide both sides by 3 to find [tex]\( x \)[/tex]: [tex]\( x = 63 / 3 = 21 \)[/tex].
- The number is 21.
3. A light flashes every 6 minutes and a bell rings every 8 minutes. How many minutes must elapse before this re-occurs?
- To find when both the light and bell will occur at the same time again, we need the Least Common Multiple (LCM) of 6 and 8.
- The LCM of 6 and 8 is 24.
- Therefore, they will both occur together every 24 minutes.
4. What is the difference between the LCM and GCF of 5, 10, and 35?
- First, find the Least Common Multiple (LCM) of 5, 10, and 35.
- The LCM of these numbers is 70.
- Next, find the Greatest Common Factor (GCF) of 5, 10, and 35.
- The GCF of these numbers is 5.
- The difference between the LCM and GCF is: 70 - 5 = 65.
These are the solutions for each part of the question.
1. What day of the week will it be 75 days from today if today is Wednesday?
- Today is Wednesday.
- There are 7 days in a week.
- To find out what day of the week it will be in 75 days, calculate the remainder of 75 divided by 7 (75 % 7).
- 75 divided by 7 gives a remainder of 5.
- Moving 5 days forward from Wednesday:
- Wednesday -> Thursday (1),
- Thursday -> Friday (2),
- Friday -> Saturday (3),
- Saturday -> Sunday (4),
- Sunday -> Monday (5).
- So, in 75 days, it will be Monday.
2. If thrice a number decreased by 10 equals 53, find the number.
- Let the number be [tex]\( x \)[/tex].
- The equation is: [tex]\( 3x - 10 = 53 \)[/tex].
- Add 10 to both sides to get: [tex]\( 3x = 63 \)[/tex].
- Divide both sides by 3 to find [tex]\( x \)[/tex]: [tex]\( x = 63 / 3 = 21 \)[/tex].
- The number is 21.
3. A light flashes every 6 minutes and a bell rings every 8 minutes. How many minutes must elapse before this re-occurs?
- To find when both the light and bell will occur at the same time again, we need the Least Common Multiple (LCM) of 6 and 8.
- The LCM of 6 and 8 is 24.
- Therefore, they will both occur together every 24 minutes.
4. What is the difference between the LCM and GCF of 5, 10, and 35?
- First, find the Least Common Multiple (LCM) of 5, 10, and 35.
- The LCM of these numbers is 70.
- Next, find the Greatest Common Factor (GCF) of 5, 10, and 35.
- The GCF of these numbers is 5.
- The difference between the LCM and GCF is: 70 - 5 = 65.
These are the solutions for each part of the question.
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