Here are two more problems I have for homework tonight. I have gotten answers, but I used "guess-and-check" and could not find an equation like I am supposed to. If you answer, please tell me if my answer is correct, walk me through your way of solving it, and if you can, show me an equation. Thanks!
#1: In a basketball game, the United States has four times as many points as Croatia. A Croatian makes a basket for three points, at which point the United States only has three times as many points. How many points does the United States have?
Here is the equation that I have:
3c + 9 = 4c
Which is a simplifyed version of:
3(c+3) = 4c.
Are my equations correct? The answer I got was 36 points.
#2: Sue has $3.08 in pennies, nickels, and quarters. She has four more pennies than quarters and one more nickel than pennies. How many nickels does she have?
I do not know the equation for this one. My answer was 14 nickels.
Again, thank you so much for any help you can give me!
#1 is correct
#2.
<<She has four more pennies than quarters> ----> q = p-4
<<one more nickel than pennies> ----> n = p+1
Now form the value equation :
25q + 5n + p = 308
25(p-4) + 5(p+1) + p = 308
take it from there
(your 14 nickels is correct, 13 pennies and 9 quarters)
Thank you so much for your help! :)
keep it clean here.
Could you please explain why the equation for the first answer is 3(c+3) and not 4c - 3??
oh wait your first answer is incorrect, sorry for a 15yrs delay, i was 1yrs old when u asked that question...
anyways, lets say croatia has 21points, and the US has 84points which is 4C, when croatia scores a basket worth 3 points they now have 24points but the US has 4C - 3, not plus (but minus) so that our answer stays 84 points for the US team and not 87.
now back to the question,
1....... U = 4C
2........U = 4C - 3 = 3C (when crotia scores that basket the US will only have 3 times as much points)
C = 3, U = 4(3)-4 = 12-3 = 9, the answer for US points in the game after Croatia scored the basked is 9 points, and before they scored the basket (which i think is not required by the question), US points is 12.
Thanks
Let's go through both problems step by step and find the answers together.
#1: In this problem, we have two pieces of information: the United States has four times as many points as Croatia, and when a Croatian makes a basket for three points, the United States only has three times as many points. Let's break it down.
Let's say the number of points Croatia has is denoted by 'c'. Since the United States has four times as many points as Croatia, we can say the number of points the United States has is 4c.
When a Croatian makes a basket for three points, the United States has three times as many points. This can be represented as:
3 + 3c = 3*(4c)
Now, let's simplify the equation. Distribute the 3 on the right side of the equation:
3 + 3c = 12c
Next, let's isolate the 'c' term on one side of the equation. Subtract 3c from both sides:
3 = 12c - 3c
This simplifies to:
3 = 9c
Finally, divide both sides by 9 to solve for 'c':
3/9 = c
c = 1/3
So, Croatia has 1/3 of a point. Now, let's find out how many points the United States has.
Using the equation 4c, substitute c = 1/3:
4 * (1/3) = 4/3
Therefore, the United States has 4/3 points, which is approximately 1.33 points.
It seems like there might have been a mistake made while solving the equation. The correct answer is not 36 points. Instead, the United States has approximately 1.33 points.
#2: In this problem, we need to find the number of nickels Sue has given that she has a total of $3.08 in pennies, nickels, and quarters. Let's break it down.
Let's denote the number of quarters Sue has as 'q', the number of pennies as 'p', and the number of nickels as 'n'.
From the problem, we know that Sue has four more pennies than quarters:
p = q + 4
We also know that Sue has one more nickel than pennies:
n = p + 1
Now, let's calculate the total value of the coins Sue has:
The total value of quarters is 25 cents times the number of quarters, which is 25q cents.
The total value of pennies is 1 cent times the number of pennies, which is 1p cents.
The total value of nickels is 5 cents times the number of nickels, which is 5n cents.
The problem states that the total value of all the coins is $3.08. We can write this as:
25q + 1p + 5n = 308 cents
From the equations we derived earlier, we can substitute the expressions for p and n:
25q + 1(q + 4) + 5(q + 4 + 1) = 308
Let's simplify this equation:
25q + q + 4 + 5q + 20 = 308
Combine like terms:
31q + 24 = 308
Subtract 24 from both sides:
31q = 308 - 24
31q = 284
Finally, divide both sides by 31 to solve for 'q':
q = 284 / 31
The result is approximately 9.16, so it seems there's a fraction of a quarter. However, since Sue cannot have a fraction of a quarter, we can conclude that there might have been a mistake in the equation or initial conditions provided.
Unfortunately, we cannot determine the number of nickels from the given information, so we can't verify the answer of 14 nickels.
I hope this explanation helps you understand the thought process and approach to solving these types of problems.