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
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1.) To find the number, let's set up an equation based on the given information. We are told that "A number decreased by 32 is -58." So, we can write the equation as follows:
x - 32 = -58
Here, x represents the unknown number we are trying to find. To isolate x, we need to undo the subtraction of 32. We can do this by adding 32 to both sides of the equation:
x - 32 + 32 = -58 + 32
Simplifying this equation gives us:
x = -26
Therefore, the number is -26.
2.) The problem states that "The product of 14 and n is -28." In algebraic terms, we can represent the product as follows:
14n = -28
To solve for n, we divide both sides of the equation by 14:
14n/14 = -28/14
Simplifying this equation gives us:
n = -2
Therefore, the algebraic equation is 14n = -28 and the value of n is -2.
3.) Let's represent the price of the red bike as "x" in dollars. Since the blue bike is $14 less than the red bike, its price would be "x - 14" dollars. The problem also states that the sum of their prices is $300. So, we can set up the equation as:
x + (x - 14) = 300
Simplifying this equation gives us:
2x - 14 = 300
To isolate x, we can add 14 to both sides of the equation:
2x - 14 + 14 = 300 + 14
Simplifying this equation gives us:
2x = 314
Next, we divide both sides of the equation by 2 to solve for x:
(2x)/2 = 314/2
Simplifying this equation gives us:
x = 157
Therefore, the price of the red bike is $157.
4.) Let's represent Emma's age as "x" years. Since Alex is six years older than Emma, his age would be "x + 6" years. The problem states that the sum of their ages is 32. So, we can set up the equation as:
x + (x + 6) = 32
Simplifying this equation gives us:
2x + 6 = 32
To isolate x, we can subtract 6 from both sides of the equation:
2x + 6 - 6 = 32 - 6
Simplifying this equation gives us:
2x = 26
Next, we divide both sides of the equation by 2 to solve for x:
(2x)/2 = 26/2
Simplifying this equation gives us:
x = 13
Therefore, Emma is 13 years old and Alex is 13 + 6 = 19 years old.
5.) Let's represent Mousy's age as "x" years. Since Mrs. Computer is 3 times older than her daughter Mousy, her age would be "3x" years. The problem states that the sum of their ages is 52. So, we can set up the equation as:
x + 3x = 52
Simplifying this equation gives us:
4x = 52
To isolate x, we can divide both sides of the equation by 4:
(4x)/4 = 52/4
Simplifying this equation gives us:
x = 13
Therefore, Mousy is 13 years old.
6.) Let's represent Tom's age as "x" years. Since Mike is 5 years more than twice as old as Tom, his age would be "2x + 5" years. The problem states that the sum of their ages is 65. So, we can set up the equation as:
x + (2x + 5) = 65
Simplifying this equation gives us:
3x + 5 = 65
To isolate x, we can subtract 5 from both sides of the equation:
3x + 5 - 5 = 65 - 5
Simplifying this equation gives us:
3x = 60
Next, we divide both sides of the equation by 3 to solve for x:
(3x)/3 = 60/3
Simplifying this equation gives us:
x = 20
Therefore, Tom is 20 years old and Mike is 2(20) + 5 = 45 years old.
7.) The sum of three consecutive integers is 108. Let's represent the first consecutive integer as "x" and the second consecutive integer as "x + 1". Using this pattern, the third consecutive integer would be "x + 1 + 1 = x + 2".
So, the equation that represents the sum of the three consecutive integers is:
x + (x + 1) + (x + 2) = 108
Simplifying this equation gives us:
3x + 3 = 108
Therefore, the correct equation to solve this word problem is 3x + 3 = 108.