So I have this problem:
Dave can vote. (18 or over.) Dave is 5 years older than Jim. Jim is not old enough to vote. Write a mathematical inequality expressing Dave's age. (Hint: determine Dave's maximum and minimum age.)
So I have his minimum age as 18 and his maximum age as 22. That's how old he can be while the other is too young to vote. But how do I write the inequality?
let J=Jim's age
let D=Dave's age
It is given that Dave can vote.
So
D>=18
Dave is 5 years older
J+5=D
or
J=D-5
Jim can't vote.
J<18
Substitute for Jim's age:
D-5<18
Solve this for the upper limit for Dave's age.
To write the inequality expressing Dave's age, let's assign a variable to Jim's age. Let's call Jim's age "J". Since Jim is not old enough to vote, he must be younger than 18. Therefore, Jim's age can be expressed as: J < 18.
Now, we also know that Dave is 5 years older than Jim. So, Dave's age can be expressed as J + 5.
To find the maximum and minimum age for Dave, we consider the age range in which Jim is not old enough to vote. Since Jim's maximum age is 17 (because he cannot be 18 or older), we can substitute J = 17 into Dave's age expression, giving us: Dave's age = 17 + 5 = 22.
Therefore, Dave's maximum age is 22.
Similarly, for Dave's minimum age, we substitute J = 0 (the youngest age Jim can be) into Dave's age expression: Dave's age = 0 + 5 = 5.
Therefore, Dave's minimum age is 5.
Hence, the mathematical inequality expressing Dave's age is:
5 ≤ Dave's age ≤ 22.
To write the mathematical inequality expressing Dave's age, we first need to assign variables to Dave and Jim's ages.
Let's say Dave's age is represented by the variable D, and Jim's age is represented by the variable J.
We know that Dave is 5 years older than Jim, so we can express this as D = J + 5.
Since Jim is not old enough to vote, we can assume that he is under 18 years old. Therefore, we can say J < 18.
Now, to determine the mathematical inequality expressing Dave's age, we need to find the minimum and maximum age for Dave given these conditions.
Minimum age: Jim's age should be just below the voting age of 18. So we can substitute J = 17 into the equation D = J + 5:
D = 17 + 5 = 22.
Maximum age: Jim's age should be the maximum possible age where he is still under 18. This is achieved when J = 17. Plugging this into the equation D = J + 5:
D = 17 + 5 = 22.
Therefore, Dave's minimum and maximum age, while Jim is not old enough to vote, is 22.
The mathematical inequality expressing Dave's age can be written as:
D ≤ 22.
So, Dave's age must be less than or equal to 22 for him to be 5 years older than Jim, while Jim is not old enough to vote.