okay so i was given a worksheet with 15 word problems. i couldn't solve 2 so if you could help me out it would be good..
If you ask Catwoman how many cats she has, she answers with the riddle, 'five-sixths of my cats plus seven.' how many cats does she have?
Abby, Britt, Christina, and Danny play with a deck of 32 cards. Danny deals them out unequally and then says, 'if we want to all have the same number of cards, abby should divide half her cards between britt and christina. then britt should do the same with christina and abby,, then christina should divide half of her cards between abby and britt.' how did danny initially distribute the cards??
thanks! im really stumped so anythhing can help.
i posted this yesterday. megan said 13 cats but i don't understand why and i still have no clue for the other problem. ive been trying to solve it and its not working! PLEASE HELP!
Brennan
ok...so 5/6 of the cats (x) + 7
therefore (5/6)x+7=x
subtract (5/6)x from each side
7=(1/6)x
times each side by 6
x = 42
so a+b+c+d = 32
a=(1/2)b+(1/2)c
b=(1/2)c+(1/2)a
c=(1/2)a+(1/2)b
and d=(1/4)32
therefore d=8
and a+b+c=(32-8)=24
next, substitute to find the equations.
hope I could help!
Sure, I'll be happy to help you with these two word problems!
1. Catwoman and her Cats:
To solve the first problem about Catwoman and her cats, let's break it down step by step:
- Let's assume the number of cats Catwoman has is represented by the variable "x."
- According to the riddle, Catwoman says "five-sixths of my cats plus seven." We can represent this in an equation as: (5/6)x + 7.
- The equation states that when we multiply the number of cats by five-sixths (5/6) and then add seven, it equals the actual number of cats Catwoman has.
- Solving for x, we need to isolate the variable: (5/6)x = x - 7.
- To isolate x, we can start by multiplying both sides of the equation by 6, which will cancel out the fraction: 5x = 6(x - 7).
- Distribute on the right side of the equation: 5x = 6x - 42.
- Now, subtract 6x from both sides: -x = -42.
- To solve for x, divide both sides of the equation by -1: x = 42.
- So, Catwoman has 42 cats.
2. Danny and the Card Distribution:
For the second problem, let's break it down step by step as well:
- Let's assume that the number of cards each person initially receives is represented by the variables "a" (Abby), "b" (Britt), and "c" (Christina).
- According to the description, Danny suggests that Abby should divide half her cards between Britt and Christina. This means that Abby gives away a/2 cards to both Britt and Christina, so Abby is left with a - (a/2) - (a/2) cards, which simplifies to a/2 cards.
- Similarly, Britt gives away b/2 cards to both Abby and Christina, so Britt is left with b - (b/2) - (b/2) cards, which simplifies to b/2 cards.
- Lastly, Christina gives away c/2 cards to both Abby and Britt, so Christina is left with c - (c/2) - (c/2) cards, which simplifies to c/2 cards.
- The problem states that they all end up with the same number of cards, which means a/2 = b/2 = c/2. We can solve this by equating any two ratios.
- Let's equate a/2 and b/2: a/2 = b/2. Cross-multiplying, we get a = b.
- Now, let's equate b/2 and c/2: b/2 = c/2. Cross-multiplying, we get b = c.
- Combining these results, we have a = b = c.
- Therefore, initially, Danny distributed the cards equally: a = b = c.
I hope these explanations help you understand how to solve these word problems! If you have any further questions, feel free to ask.