Write a story or situation that can be represented by the given equation.
4a + 5 = 12a - 11
I know I supposed to compare like terms, but how do I write it out???
Joe's tickets cost $5 to get to the game and $4 each for a tickets
Mac gets an $11 discount in the taxi but pays $12 each for a tickets
What number of tickets , a , costs Joe and Mac the same?
you just need to include the different #s and how they are solved so you can do 12a __________your story________________but you need to do - 11 you have to do the proper equations
Ok thanks!
Once upon a time, in a land filled with numbers and equations, there was a delightful equation called 4a + 5 = 12a - 11. This equation was quite mischievous; it loved to play tricks on anyone who dared to solve it.
One day, a brave mathematician decided to take on the challenge. With a determined look on their face, they proclaimed, "I shall solve this equation, no matter how tricky it may be!"
They began by comparing the like terms. "Hmm, 4a and 12a are like terms, but they have different coefficients," the mathematician mused. "It's like comparing apples and oranges!"
Undeterred, the mathematician focused on the constants. "5 and -11 are both constants, but they are different in value. It's like comparing a sunny day to a thunderstorm!"
Putting on their thinking cap, the mathematician had an idea. "What if I move all the terms with 'a' to one side, and all the constants to the other side? Then, I can see if there's a solution hiding in plain sight!"
They proceeded to subtract 12a from both sides of the equation. "Now, I have -8a + 5 = -11. It's like making a hotdog disappear from the dinner table!"
With a flick of their mathematical wand, the mathematician then subtracted 5 from both sides. "Voilà! -8a = -16. It's like magic!"
Finally, dividing both sides of the equation by -8, the mathematician arrived at the solution. "Aha! a = 2. It's like finding the pot of gold at the end of a rainbow!"
And so, our brave mathematician succeeded in taming the mischievous equation, 4a + 5 = 12a - 11, using their wit, humor, and some mathematical tricks. From that day forward, their name was beloved among all for solving the equation that once brought confusion to the land.
To write out the equation and understand the story or situation it represents, let's break it down step by step.
1. Given equation: 4a + 5 = 12a - 11
2. Start by comparing like terms, which means grouping all the terms with 'a' on one side and the constants on the other side.
- To do this, let's first move the constant terms (5 and -11) to the opposite side of the equation by subtracting 5 from both sides:
4a + 5 - 5 = 12a - 11 - 5
This simplifies to: 4a = 12a - 16
3. Next, let's move all the 'a' terms to the left side by subtracting 12a from both sides:
4a - 12a = 12a - 16 - 12a
Simplifying further: -8a = -16
4. Now, to find the value of 'a', divide both sides of the equation by -8:
-8a / -8 = -16 / -8
This gives us: a = 2
Now, let's consider the story or situation described by this equation:
Imagine you have a situation where you have two groups of objects, represented by 'a'. Initially, one group has 4 objects, and you add 5 more objects to it. On the other hand, the second group initially has 12 times the number of objects as the first group, but you subtract 11 objects from it.
The equation 4a + 5 = 12a - 11 represents the state where both groups end up having the same number of objects, and we need to find the value of 'a' (the number of objects in each group) to solve the equation. In this particular scenario, 'a' would equal 2, meaning each group has 2 objects.