Please help me to solve this word problem. How do I write and equation and solve? Find three consecutive even integers such that 50 times the smallest is 88 less than 46 times the largest
a = smallest number
b = middle number = a + 2
c = largest number = b + 2 = a + 2 + 2 = a + 4
50 times the smallest is 88 less than 46 times the largest, mean:
50 a = 46 c - 88
Now:
50 a = 46 ( a + 4 ) - 88
50 a = 46 ∙ a + 46 ∙ 4 - 88
50 a = 46 a + 184 - 88
50 a = 46 a + 96
Subtract 46 a
to both sides
50 a - 46 a = 46 a + 96 - 46 a
4 a = 96
Divide both sides by 4
a = 96 / 4 = 24
b = a + 2 = 24 + 2 = 26
c = a + 4 = 24 + 4 = 28
The numbers are:
24 , 26 and 28
To solve this word problem, we can follow these steps:
Step 1: Understand the problem
Let's assume the smallest even integer is 'x'. Since we are looking for three consecutive even integers, the next two even integers would be 'x + 2' and 'x + 4'.
Step 2: Set up the equation
According to the problem, "50 times the smallest is 88 less than 46 times the largest". We can translate this into an equation.
50x = 46(x + 4) - 88
Step 3: Solve the equation
To solve the equation, we will start by expanding the right side of the equation.
50x = 46x + 184 - 88
Combine like terms.
50x = 46x + 96
Next, subtract 46x from both sides of the equation.
50x - 46x = 46x + 96 - 46x
Simplify.
4x = 96
Now, divide both sides of the equation by 4 to isolate 'x'.
4x / 4 = 96 / 4
Simplify.
x = 24
So, the smallest even integer is 24. The next two consecutive even integers would be 26 and 28.
The three consecutive even integers are 24, 26, and 28.