Math  /  Algebra

QuestionWhat everyday life situation might each of these equations describe? a) 5(18)=t5-(-18)=t \rightarrow b) 36+(20)=t-36+(-20)=t c) 84=t-8-4=t d) 100(15)=t100-(-15)=t

Studdy Solution

STEP 1

What is this asking? We need to come up with real-world scenarios that match each of these addition and subtraction problems with negative numbers. Watch out! Don't mix up addition and subtraction, and be careful with those negative signs!
A double negative makes a positive!

STEP 2

1. Scenario A
2. Scenario B
3. Scenario C
4. Scenario D

STEP 3

Alright, let's tackle the first equation: 5(18)=t5 - (-18) = t.
What's going on here?
We're subtracting a negative number.

STEP 4

Remember, subtracting a negative is the same as adding a positive!
So, 5(18)5 - (-18) becomes 5+185 + 18.

STEP 5

5+18=235 + 18 = 23

STEP 6

So, t=23t = 23.
Think of it like this: You owe someone $5\$5.
They decide to forgive $18\$18 of debt.
It's like they *gave* you $18\$18, and now you have $23\$23 more than you did before!

STEP 7

Next up: 36+(20)=t-36 + (-20) = t.
We're adding two negative numbers together.

STEP 8

When we add two negatives, the result is even *more* negative!

STEP 9

36+(20)=56-36 + (-20) = -56

STEP 10

So, t=56t = -56.
Imagine you're playing a game.
You lose **36** points in the first round and then lose another **20** points in the second round.
Your total score?
A disheartening 56-56 points!

STEP 11

Now for 84=t-8 - 4 = t.
We're starting with a negative number and subtracting a positive number.

STEP 12

This is like digging yourself deeper into a hole!

STEP 13

84=12-8 - 4 = -12

STEP 14

So, t=12t = -12.
Imagine the temperature is already a chilly 8-8 degrees.
Then, it drops another **4** degrees.
Brrr! The new temperature is a frigid 12-12 degrees!

STEP 15

Finally, let's look at 100(15)=t100 - (-15) = t.
Again, we're subtracting a negative number.

STEP 16

Just like before, subtracting a negative is the same as adding a positive!
So, 100(15)100 - (-15) becomes 100+15100 + 15.

STEP 17

100+15=115100 + 15 = 115

STEP 18

So, t=115t = 115.
Imagine you have $100\$100 in your bank account.
The bank accidentally charged you a $15\$15 fee, but they quickly correct their mistake and remove the charge.
It's like they *gave* you $15\$15, so now you have $115\$115!

STEP 19

a) t=23t = 23 (Example: Forgiving a debt) b) t=56t = -56 (Example: Losing points in a game) c) t=12t = -12 (Example: Temperature dropping) d) t=115t = 115 (Example: Bank error correction)

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