1. The sum of 3 consecutive odd numbers is 39.
2. Mrs. Gardner went to the market. She purchased some lettuce heads and some tomatoes. There were 12 items purchased. She bought twice as many tomatoes as lettuce heads.
3. 3 times the first of three consecutive numbers is 4 more than 2 times the second.
help me please (:
(n-2) + n + (n+2) = 39
3 n = 39
n = 13
so
12 , 13 , 14
L + 2 L = 12
3 L = 12
L = 4 heads of lettuce
2 L = 8 tomatoes
(n-1), n , (n+1)
3(n-1) - 4 = 2 n
3 n - 3 - 4 = 2 n
n = 7
so
6 , 7 , 8
Three consecutive integers are such that when they are taken in increasing order and
multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.
Its answer is 7,8,9
1. To find the three consecutive odd numbers, we first need to define a variable. Let's call the first odd number "x". Since the numbers are consecutive, the second odd number would be "x + 2" and the third odd number would be "x + 4". We are given that the sum of these three numbers is 39, so we can write the equation as:
x + (x + 2) + (x + 4) = 39
Now, we can solve for x by simplifying the equation:
3x + 6 = 39
Subtract 6 from both sides of the equation:
3x = 33
Divide both sides by 3:
x = 11
Therefore, the three consecutive odd numbers are 11, 13, and 15.
2. Let's define two variables: the number of lettuce heads as "L" and the number of tomatoes as "T". We are given that Mrs. Gardner bought twice as many tomatoes as lettuce heads, so we can write the equation as:
T = 2L
We are also given that she purchased a total of 12 items, which means the sum of lettuce heads and tomatoes is 12. We can write another equation as:
L + T = 12
Now, we can substitute the value of T from the first equation into the second equation:
L + 2L = 12
Combining like terms, we have:
3L = 12
Divide both sides by 3:
L = 4
Now, we can substitute this value of L back into the first equation to find T:
T = 2(4)
T = 8
Therefore, Mrs. Gardner bought 4 lettuce heads and 8 tomatoes.
3. Let's define three consecutive numbers as "x", "x + 1", and "x + 2". We are given that 3 times the first number is 4 more than 2 times the second number. We can write this as an equation:
3x = 2(x + 1) + 4
Now, we can solve for x by simplifying the equation:
3x = 2x + 2 + 4
Combine like terms:
3x = 2x + 6
Subtract 2x from both sides:
x = 6
Therefore, the first consecutive number is 6, the second is 7, and the third is 8.