Question

Dai is comparing how many trading cards he has with his friend Maura. Initially, they find that Dai has four more cards than twice the number that Maura has. Part B) If Dai must give Maura 8 cards so that they have the same amount, set up and solve an equation to determine the number of cards Maura initially had.

Answer 1

Maura had 12 cards initially

Explanation:

Represent Dai's card with D and Maura's card with M.

From the first statement, we understand that:

D = 4 more that twice of M

This is represented as:

D = 4 + 2M

From the second statement, we understand that.

When 8 is subtracted from D, M is increased by 8 and both are equal.

This is represented as:

D - 8 = M + 8

Hence, the equations of the system is:

D = 4 + 2M

D - 8 = M + 8

Substitute 4 + 2M for D in the second equation

4 + 2M - 8 = M + 8

Collect like terms

2M - M = 8 - 4 + 8

M = 12

To solve for D, we simply substitute 12 for M in D = 4 + 2M

D = 4 + 2 * 12

D = 4 + 24

D = 28

Hence, Maura had 12 cards initially