SOLUTION: John's age is 3 times more than twice his younger brother's age. If the sum of their ages is at most 18, write an equation to express possible ages for John. This is a question

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Question 1128059: John's age is 3 times more than twice his younger brother's age. If the sum of their ages is at most 18, write an equation to express possible ages for John.
This is a question my Algebra 1 teacher has given me, I've tried every equation that I have thought of and every time she's told me I'm wrong. Please help
Found 2 solutions by MathLover1, htmentor:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let's John's age be x and his brother's age be y
if John's age is 3 times more than twice his younger brother's age, we have (I guess it's 3 more, not 3 timesmore)
x=2y%2B3...eq.1
If the sum of their ages is+at most 18, write an equation to express possible ages for John,
x%2By%3C=18....eq.2 ...(since given +at most 18)
now you can substitute x from eq.1 in eq.2 and solve for y
2y%2B3%2By%3C=18
3y%3C=18-3
y%3C=15%2F3
y%3C=5-> his brother's age is 5

now go to x=2y%2B3...eq.1 and find John's age

x=2%2A5%2B3...eq.1
x=13->John's age


Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you mean 3 more than twice his brother's age instead of 3 times more.
Let x = the younger brother's age, y = John's age
y = 3 + 2x -> x = y/2 - 3/2
x + y <= 18 y <= 18 - x -> y <= 18 - y/2 + 3/2
Solve the inequality for y:
3y/2 <= 39/2
y <= 13
So John's age is less than or equal to 13