1.)The product of 14 and n is -28. Write the algebraic equation.

2.)Four times a certain number is the same as the number increased by 78

3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike

4.)Alex is six years older than his sister, Emma. The sum of their ages is 32. How old is Alex?

5.)Mrs. Computer is 3 times older than her daughter, Mousy. The sum of their ages is 52. How old is Mousy?

6.)Mike is 5 years more than twice as old as Tom. The sum of their ages is 65. How old is Mike

7.)The sum of three consecutive integers is 108. Which equation would be used to solve this word problem? (HINT: The equation has been simplified some..

8.)Find two consecutive odd integers whose sum is 72. Which equation would be used to solve this problem? (HINT: The equation has been simplified some

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no ideas on any of these? Even with the hints?

1.) 14n = -28

6.) m = 2t+5
m+t = 65, so t=65-m
m = 2(65-m)+5
...

2) 4x = x - 78

3) b + r = 330 and b = r -14
These could be combinte by replacing the b with r - 14

r - 14 + r= 330

4) A = E + 6
A + E = 32

5) C = 3M
C + M = 52

6) n = 1st integer, n + 1 = 2nd and n+2 = the 3rd integer

sum is: n + n + 1 + n + 2= 105

7. Consecutive odd or consecutive even integers differ by 2. Example, 1, 3, 5 or 2, 4, 6
With this hint, can you figure this out. It is similar to 6.

1.) The product of 14 and n is -28. Write the algebraic equation.

To find the algebraic equation for this problem, we can use the formula for the product of two numbers: a * b = c.
In this case, we know that a = 14 and c = -28. The value of b is the unknown, represented by n. Therefore, the algebraic equation is:
14 * n = -28.

2.) Four times a certain number is the same as the number increased by 78.
To write the algebraic equation for this problem, we can use the formula for multiplication and addition. Let's assume the certain number is represented by x. The equation can be written as:
4x = x + 78.

3.) A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike?
Let's assume the price of the red bike is represented by x. Since the blue bike is $14 less than the red bike, the price of the blue bike can be represented as x - 14. The sum of their prices is $300, so we can write the equation:
x + (x - 14) = 300.

4.) Alex is six years older than his sister, Emma. The sum of their ages is 32. How old is Alex?
Let's assume Emma's age is represented by x. Since Alex is six years older, his age can be represented as x + 6. The sum of their ages is 32, so we can write the equation:
x + (x + 6) = 32.

5.) Mrs. Computer is 3 times older than her daughter, Mousy. The sum of their ages is 52. How old is Mousy?
Let's assume Mousy's age is represented by x. Since Mrs. Computer is three times older, her age can be represented as 3x. The sum of their ages is 52, so we can write the equation:
x + 3x = 52.

6.) Mike is 5 years more than twice as old as Tom. The sum of their ages is 65. How old is Mike?
Let's assume Tom's age is represented by x. Since Mike is 5 years more than twice Tom's age, his age can be represented as 2x + 5. The sum of their ages is 65, so we can write the equation:
x + (2x + 5) = 65.

7.) The sum of three consecutive integers is 108. Which equation would be used to solve this word problem? (HINT: The equation has been simplified some.)
To find three consecutive integers, we can assume the smallest integer as x. The next consecutive integer would be (x + 1), and the one after that would be (x + 2). The sum of these three integers is 108, so we can write the equation:
x + (x + 1) + (x + 2) = 108.

8.) Find two consecutive odd integers whose sum is 72. Which equation would be used to solve this problem? (HINT: The equation has been simplified some.)
To find two consecutive odd integers, we can assume the smallest odd integer as x. The next consecutive odd integer would be (x + 2), since the difference between consecutive odd numbers is 2. The sum of these two integers is 72, so we can write the equation:
x + (x + 2) = 72.