1. In an ordered set of 4 consecutive odd integers, the sum of 3 times the second integer and the greatest integer is 104. Which is the least integer in the set?
Choices: 11, 17, 19, 23, 27
2. How old is David if his age 6 years from now will be twice his age 7 years ago?
3. If the value of n nickels plus d dimes is c cents, what is n in terms of d and c?
Thank you so much! It'll mean a lot to me if you answer all three of these questions!
1. Why not just see which one works?
Try 11. Is (3x13)+ 17 = 104? No
So, try the 23.
Is (3x25)+ 20 = 104? Yes
Does anybody know 2 and 3?
2. Let x represent his current age. Solve for x.
x + 6 = 2x - 7
3.
n + d = c
n = c - d
3.
5n + 10d = c
5n = c - 10d
n = c/5 - 2d
1. To solve this problem, we need to set up an equation using the information given. Let's call the first odd integer x. Since the set consists of 4 consecutive odd integers, the second odd integer would be x + 2, the third would be x + 4, and the fourth (or the greatest) would be x + 6.
Now, according to the problem, the sum of 3 times the second integer (3(x + 2)) and the greatest integer (x + 6) is 104. We can write this as an equation:
3(x + 2) + (x + 6) = 104
Now, solve this equation to find the value of x, which will be the least integer in the set.
2. To find David's current age, we need to set up an equation using the information given. Let's call David's current age x.
According to the problem, David's age 6 years from now will be twice his age 7 years ago. We can write this as an equation:
x + 6 = 2(x - 7)
Now, solve this equation to find the value of x, which will be David's current age.
3. To find the value of n in terms of d and c, we need to consider the information given. The problem states that the value of n nickels plus d dimes is equal to c cents.
A nickel is worth 5 cents, so the value of n nickels would be 5n cents. Similarly, a dime is worth 10 cents, so the value of d dimes would be 10d cents.
According to the problem, the sum of these values is equal to c cents. We can write this as an equation:
5n + 10d = c
Now, solve this equation to express n in terms of d and c.