Card Collecting

Question

Andre, Laura, and Danielle each collect baseball cards.

 Andre has three more than double the number of cards that Danielle has.

 Laura has four fewer cards than Danielle.

 All together they have a total of 43 cards.

Use an equation to determine the number of cards that each person has in their collection. Show your work.

Answer 1

In order to set up a problem with three unknowns like this, look for the person that everybody else is being compared to. Notice that Andre is described in terms of Danielle, and Laura is described in terms of Danielle, but Danielle is not described in terms of anyone. That makes Danielle our variable, and it means we only need one variable instead of three.

So let d be the number of cards Danielle has.

Andre has three more than double Danielle, so we double d and then add three:

Andre = 2d + 3

Laura has four fewer than Danielle, so we subtract:

Laura = d - 4

Remember, we know all three collections together come to 43, so we add up everything and set it equal to 43:

d + (2d + 3) + (d - 4) = 43

Now combine like terms. The d, the 2d and the other d give 4d, and the +3 and -4 give -1:

4d - 1 = 43

Adding 1 to both sides and then dividing by 4:

4d = 44

d = 11

Now we go back and answer the actual question, since the problem asked for all three people and not just d. Danielle has 11. Andre has 2(11) + 3 = 25. Laura has 11 - 4 = 7.

It is always worth checking against the original sentence. 11 + 25 + 7 = 43, which matches, and 25 really is three more than double 11.

So, our final answer is that Danielle has 11 cards, Andre has 25, and Laura has 7.

Answer 2

First, note that three equations is sufficient to determine the values of three variables. Let A, L, and D represent the number of baseball that each has.

1) A = 2D + 3

2) L = D - 4

3) A + D + L = 43

After studying the three formulas, you may notice that D appears on the right side of equations (1) and (2), so we may re-write equation (3) as:

(2D + 3) + D + (D - 4) = 43

4D -1 = 43

D = 11

Now, use that value of D with equation (1) and (2) to find the other values.

IMPORTANT: Be sure to check your answer by substitution the values of A, D, and L into the three equtions to verify that your answer work.

Answer 3

d represents the number of cards Danielle has

2d + 3 represents the number of cards Andre has

d - 4 represents the number of cards Laura has

d + 2d + 3 + d - 4 = 43

Can you solve for d and answer?