The sum of two even consecutive integers is 114. What is the smallest integer?
1 answer:
Answer:
56
Step-by-step explanation:
The sum of two <em>even</em> consecutive integers is 114.
Let's let the first even integer be 2n, where n is <em>some</em> integer: it doesn't matter what n is, but if we multiply n by 2, we are certainly getting an even number. This is because any integer multiplied by 2 is even.
So, this means that the second number is 2n+2.
Their sum is 114. In other words:
Solve for n.
Combine like terms:
Subtract 2 from both sides:
Divide both sides by 4:
So, n is 28.
This means that the first number is 28(2) or 56.
And the second number is 58.
So, the smallest integer is 56.
And we're done!
You might be interested in
Answer:
A. 605 mL of the 35% solution
B. 55 mL of the 95% solution
Step-by-step explanation:
It is given that, you need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture.
Let x and y be the amount of 35% alcohol solution and 95% alcohol solution (in mL) respectively.
So,
Amount equation: ...(1)
Alcohol equation : ...(2)
On solving (1) and (2), we get
Now, substitute y=55 in (1).
Therefore, we need 605 mL of the 35% solution and 55 mL of the 95% solution.