add or subtract a positive integer on a number line
1. ms. howard buys a car for $500 and adds a music system that costs $200. then she adds a pair of seat covers for the price shown. how much has ms. howard spent on the car so far?
2. at the beginning of the week, tideland manufacturing had an inventory of 60,000 screws. this week they received a shipment of 30,000 more screws. then they used 50,000 screws to make their tideland mowers. how many screws do they have left in inventory?
3. stem a chemical reaction is endothermic if it absorbs heat from its surroundings. it is exothermic if it gives off heat to its surroundings. in her chemistry class, lily is given a salt (ammonium nitrate) and a beaker of water at 60°f. she dissolves the salt in the water and sees that the temperature of the solution is now 50°f. did the temperature of the solution increase or decrease? by how many degrees? what kind of reaction has occurred? explain.
4. at the beginning of the month, joe has $180 in his bank account. he wants to buy a new gaming system for $250 in two weeks. his parents have offered to loan him money if he needs it. he gets $20 a week for an allowance. will he have enough money at the end of two weeks to make the purchase on his own? if not, how much will he have to borrow from his parents? explain.
5. reason can you ever add two positive integers and get a negative integer? explain.
6. reason can you subtract a positive integer from a positive integer and get a negative result? explain your answer.

Question

Accepted Answer

# 1. ## Step1: Add the costs The cost of the car is $500$, the music system is $200$, and the seat - covers are $50$. We need to find the total cost. $$500 + 200+50$$ ## Step2: Calculate the sum First, $500 + 200=700$, then $700 + 50 = 750$ # Answer: Ms. Howard has spent $750$ on the car so far. # 2. ## Step1: Calculate the total number of screws after receiving the shipment The initial inventory is $60000$ screws, and they received $30000$ more. So the total is $60000+30000$ $$60000 + 30000=90000$$ ## Step2: Subtract the number of screws used They used $50000$ screws. So the number of screws left is $90000 - 50000$ $$90000-50000 = 40000$$ # Answer: They have $40000$ screws left in inventory. # 3. ## Step1: Determine if the temperature increased or decreased The initial temperature of the water was $60^{\circ}F$ and the final temperature of the solution is $50^{\circ}F$. Since $50<60$, the temperature decreased. ## Step2: Calculate the change in temperature The change in temperature is $60 - 50=10^{\circ}F$ ## Step3: Determine the type of reaction Since the temperature of the solution decreased (the solution absorbed heat from the surroundings), it is an endothermic reaction. # Answer: The temperature of the solution decreased by $10^{\circ}F$. It is an endothermic reaction because the solution absorbed heat (causing the temperature to drop). # 4. ## Step1: Calculate the amount of money Joe will have after two weeks Joe has an initial amount of $180$ dollars. He gets $20$ dollars per week for two weeks. So the total amount of money he will have is $180+20\times2$ $$180 + 20\times2=180 + 40=220$$ ## Step2: Compare with the cost of the gaming system The cost of the gaming system is $250$ dollars. Since $220<250$ ## Step3: Calculate the amount he needs to borrow The amount he needs to borrow is $250 - 220 = 30$ # Answer: No, he will not have enough money. He will have to borrow $30$ dollars from his parents. # 5. ## Step1: Use the property of positive integers Let $a$ and $b$ be positive integers. By the definition of addition of positive integers, $a + b=a + b>0$ (since $a>0$ and $b>0$) # Answer: No. When you add two positive integers $a$ and $b$ ($a>0$, $b > 0$), by the rules of addition of positive numbers $a + b>0$. # 6. ## Step1: Consider the general form of subtraction of positive integers Let $a$ and $b$ be positive integers. $a−b=a+( - b)$. If $a < b$, for example, let $a = 3$ and $b=5$, then $a - b=3-5=-2$ # Answer: Yes. If the positive integer being subtracted ($b$) is greater than the positive integer from which it is subtracted ($a$) ($a < b$), then $a - b=a+( - b)$ will be negative. For example, $3-5=-2$.

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QUESTION IMAGE

Question

Explanation:

1.

Step1: Add the costs

Step2: Calculate the sum

Answer:

2.

Step1: Calculate the total number of screws after receiving the shipment

Step2: Subtract the number of screws used