Question

"Bob and Mike have 210 cards together. Mike has 24 fewer cards than Bob. How many cards does each have? Write a system to represent the situation, and then solve the system.

A) Bob has 117 cards, Mike has 93 cards
B) Bob has 117 cards, Mike has 141 cards
C) Bob has 123 cards, Mike has 99 cards
D) Bob has 141 cards, Mike has 117 cards"

Answer 1

The system of equations representing the situation where Bob and Mike have 210 cards together, and Mike has 24 fewer than Bob, is solved to find that Bob has 117 cards and Mike has 93 cards (Option A).

Step-by-step explanation:

The student is asking to solve a system of equations based on a word problem about Bob and Mike who jointly have a collection of 210 cards. Moreover, Mike has 24 fewer cards than Bob. To represent this situation, we set up two equations: let B represent the number of cards Bob has, and M represent the number of cards Mike has.

The system of equations can be written as:

• B + M = 210 (since together they have 210 cards)
• M = B - 24 (since Mike has 24 fewer cards than Bob)

We can substitute the second equation into the first to solve for B (Bob's cards):

1. B + (B - 24) = 210
2. 2B - 24 = 210
3. 2B = 234
4. B = 117

Now that we have B, we can find M:

1. M = B - 24
2. M = 117 - 24
3. M = 93

Therefore, the correct answer is: Bob has 117 cards, and Mike has 93 cards, which corresponds to option A.