I had a lot of trouble with these two questions can someone help?
george spent 25% of the moeny he had on lunch and 60% of the rmaining money on dinner. if he then had 9 dollars left, how much money did he spend on lunch and dinner?
For what set of values of x is the expression Absolute value sign 3x+4 absolute value sign < 0 true?
a) -4/3 < 0<x
b)x<-4/3
c) no real numbers
d)all real numbers
started with $x
spent .25x, leaving .75x
spent .60*.75x = .45x
so, he spent a total of .70x
.30x = 9, so he spent (.70/.30)*9 = $21
You want |3x+4| < 0
now, come on -- you know that absolute values are never negative.
So, no solutions
where did you get .70?
.70 = .25 + .45
the amounts he spent
Certainly! I can help you with those questions.
Question 1: George spent 25% of the money he had on lunch and 60% of the remaining money on dinner. If he then had 9 dollars left, we can determine how much money he spent on lunch and dinner.
To solve this problem, we can set up the following equation using algebra:
Let x represent the original amount of money George had.
George spent 25% of x on lunch, which is 0.25 * x.
Then, he had 75% (100% - 25%) of x remaining, which is 0.75 * x.
Next, George spent 60% of the remaining money on dinner, which is 0.6 * (0.75 * x).
According to the problem, he had 9 dollars left, so we have the equation:
0.75x - 0.6(0.75x) = 9
Now, we can solve this equation to find the value of x and then determine how much money he spent on lunch and dinner.
Question 2: For what set of values of x is the expression |3x + 4| < 0 true?
The absolute value of any real number is always non-negative. In other words, the absolute value cannot be less than zero. Therefore, there are no real numbers x that make the expression |3x + 4| < 0 true.
Thus, the correct answer is option c) "no real numbers."
If you have any further questions or need clarification on the solution process, please let me know!