the sun 4.5 and one third a number is equal to at mot 28.9. what are all the possible values of the number? how would you write an inequality that could used to solve this problem?

Answer 1

Let $x$ represent the number we are trying to find. According to the problem, four and one third of this number is equal to at most 28.9.

First, we need to express "four and one third" in a mathematical form. Four and one third can be written as:

$$4\frac{1}{3}=4+\frac{1}{3}=\frac{12}{3}+\frac{1}{3}=\frac{13}{3}$$

Now, we can express the equation based on the information given:

$$\frac{13}{3}x\le 28.9$$

To eliminate the fraction, we can multiply both sides of the inequality by 3 (we can do this since 3 is positive, which won't change the direction of the inequality):

$$13x\le 28.9\times 3$$

Calculating the right side:

$$28.9\times 3=86.7$$

So we have:

$$13x\le 86.7$$

Next, divide both sides by 13 to solve for $x$:

$$x\le \frac{86.7}{13}$$

Calculating $\frac{86.7}{13}$:

$$\frac{86.7}{13}\approx 6.69$$

Therefore, the inequality that represents the problem is:

$$x\le 6.69$$

Thus, all possible values of the number $x$ are those that are less than or equal to $6.69$. In conclusion, the solution to the problem is:

$$x\le 6.69$$