1.)A number decreased by 32 is -58. Find the number.
The number is ____. (Give only the value of the number as your answer.
2.)The product of 14 and n is -28. Write the algebraic equation
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?
Alex is ____ years old.
5.)Mrs. Computer is 3 times older than her daughter, Mousy. The sum of their ages is 52. How old is Mousy?
Mousy is ____ years old
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...)
3x + 3 = 108
3x = 108
3(x+3) = 108
3x + 1 = 108
#7 is badly written
If x is the smallest number, then
x + (x+1) + (x+2) = 3x+3 = 108
If is the middle number, then
(x-1) + x + (x+1) = 3x = 108
In no case are the other two choices valid.
For the others, just put the words into symbols and solve. For example,
#6: m = 5+2t, so
(5+2t)+t=65
3t+5=65
3t=60
t=20
m=45
1.) To find the number, we can set up an equation using the given information. Let's call the number "x". The problem states that a number decreased by 32 is -58. So, we can write the equation as:
x - 32 = -58
To solve for x, we can add 32 to both sides of the equation:
x - 32 + 32 = -58 + 32
This simplifies to:
x = -26
Therefore, the number is -26.
2.) The problem states that the product of 14 and n is -28. We can write the algebraic equation as:
14n = -28
3.) Let's represent the price of the red bike as "x". According to the problem, a blue bike is $14 less than a red bike, so the price of the blue bike would be x - 14. The sum of their prices is $300, so we can write the equation as:
x + (x - 14) = 300
Simplifying this equation gives:
2x - 14 = 300
Now, add 14 to both sides of the equation:
2x - 14 + 14 = 300 + 14
This simplifies to:
2x = 314
Finally, divide both sides of the equation by 2:
2x / 2 = 314 / 2
This gives:
x = 157
Therefore, the price of the red bike is $157.
4.) Let's represent Emma's age as "x". According to the problem, Alex is six years older than Emma, so Alex's age would be x + 6. The sum of their ages is 32, so we can write the equation as:
x + (x + 6) = 32
Simplifying this equation gives:
2x + 6 = 32
Now, subtract 6 from both sides of the equation:
2x + 6 - 6 = 32 - 6
This simplifies to:
2x = 26
Finally, divide both sides of the equation by 2:
2x / 2 = 26 / 2
This gives:
x = 13
Therefore, Alex is 13 + 6 = 19 years old.
5.) Let's represent Mousy's age as "x". According to the problem, Mrs. Computer is 3 times older than her daughter, so Mrs. Computer's age would be 3x. The sum of their ages is 52, so we can write the equation as:
x + 3x = 52
Simplifying this equation gives:
4x = 52
Now, divide both sides of the equation by 4:
4x / 4 = 52 / 4
This gives:
x = 13
Therefore, Mousy is 13 years old.
6.) Let's represent Tom's age as "x". According to the problem, Mike is 5 years more than twice as old as Tom, so Mike's age would be 2x + 5. The sum of their ages is 65, so we can write the equation as:
x + (2x + 5) = 65
Simplifying this equation gives:
3x + 5 = 65
Now, subtract 5 from both sides of the equation:
3x + 5 - 5 = 65 - 5
This simplifies to:
3x = 60
Finally, divide both sides of the equation by 3:
3x / 3 = 60 / 3
This gives:
x = 20
Therefore, Mike is 2(20) + 5 = 45 years old.
7.) The correct equation to solve the word problem is:
3(x+1) = 108
This equation represents the sum of three consecutive integers, with x being the first integer. The product of 3 and (x+1) is equal to 108.