Fran, Dan, and Stan have a total of 194 cards. Fran has 24 more than Dan, but 35 less than Stan. How many do each of them have? I don't know how to set this up. Thanks.
Are you sure that this is the exact wording for this problem?
Need to know info for either Dan or Stan.
You posted this almost exact same problem yesterday. I pasted that post below.
I hit 'post answer' too soon. See below.
Dan, Fran, and Stan have 194 cards. Dan has 24 less than Fran, and Stan has 35 more than Fran. How many do each of them have?
Let x = the number of cards that Fran has.
x + x - 24 + x + 35 = 194
3x + 11 = 194
3x = 183
x = 61
To solve this problem, let's start by assigning variables to the unknown quantities we're trying to find. Let's use F to represent the number of cards Fran has, D to represent the number of cards Dan has, and S to represent the number of cards Stan has.
We know that Fran has 24 more cards than Dan, so we can express this as:
F = D + 24
And we also know that Fran has 35 fewer cards than Stan, so:
F = S - 35
We're given that the total number of cards they have is 194, so we can write the equation:
F + D + S = 194
Now, we have a system of equations:
F = D + 24
F = S - 35
F + D + S = 194
To solve this system of equations, we can use substitution. Since we already have F in terms of D and S in the first two equations, let's substitute those into the third equation.
(D + 24) + D + (S - 35) = 194
Simplify the equation:
2D + S - 11 = 194
We can rearrange the equation to isolate S:
S = 194 - 2D + 11
S = 205 - 2D
Now, let's substitute this value of S back into equation 2 to solve for F:
F = S - 35
F = (205 - 2D) - 35
F = 170 - 2D
We'll substitute the expressions for F and S (in terms of D) into the first equation:
170 - 2D = D + 24
Let's solve this equation for D:
170 = 3D + 24
3D = 170 - 24
3D = 146
D = 146 / 3
D ≈ 48.67
Since we're dealing with cards, we can't have a fraction of a card. Therefore, we'll round D to the nearest whole number, which is 49.
Now, let's substitute this value of D back into the expressions for F and S to find their values:
F = 170 - 2D
F = 170 - 2(49)
F = 170 - 98
F = 72
S = 205 - 2D
S = 205 - 2(49)
S = 205 - 98
S = 107
So, Fran has 72 cards, Dan has 49 cards, and Stan has 107 cards.