Find the two consecutive odd integers such that 5 times the first integer is 12 more than 3 times the second.
can some explain to me how to get this
i was thinking the formula would be '
5x+12=3x
No, that's not it. The second integer is x+2, since it is "consecutive" and also odd
5x = 3(x+2) + 12
2x = 18
x = 9
you have to realize that consecutive odd numbers are two apart.
So if you call the first one x, the next one would be x+2
Now "translate" our English to Math
"5 times the first integer is 12 more than 3 times the second. "
..... 5x = 3(x+2) + 12
this solves to get x=9, and the first number is 9 and the second is 11
check: 5*9=45
3*11=33
45 is greater than 33 by 12
To find the two consecutive odd integers, you can follow these steps:
1. Let's denote the first odd integer as x.
2. Since the integers are consecutive, the next odd integer would be x + 2.
3. The problem states that 5 times the first integer is 12 more than 3 times the second integer. This can be expressed as the equation: 5x = 3(x + 2) + 12.
4. Simplify the equation: 5x = 3x + 6 + 12.
5. Combine like terms: 5x = 3x + 18.
6. Subtract 3x from both sides: 2x = 18.
7. Divide both sides by 2: x = 9.
Therefore, the first odd integer is 9, and the next odd integer is 9 + 2 = 11.