Question

Janae and Jerome each have m marbles. Gwen has 4(m + 2) marbles. John has 8m + 4 marbles. If John has more marbles than Janae, Jerome, and Gwen combined, how many marbles might Janae and Jerome each have? Select each possible answer.

A.
Janae and Jerome each have 1 marble.
B.


Janae and Jerome each have 2 marbles.
C.


Janae and Jerome each have 3 marbles.
D.


Janae and Jerome each have 4 marbles.
E.


Janae and Jerome each have 5 marbles.​

Answer 1

C, D, E

Explanation:

The numbers of marbles are:

• Janae - m;
• Jerome - m;
• Gwen - 4(m+2);
• John - 8m+4.

Janae, Jerome, and Gwen combined have

m + m + 4(m+2) = m + m +4m + 8 =6m + 8 marbles.

If John has more marbles than Janae, Jerome, and Gwen combined, then

`8m+4>6m+8,\\ \\8m-6m>8-4,\\ \\2m>4,\\ \\m>2.`

So, possible answers are

• Janae and Jerome each have 3 marbles;
• Janae and Jerome each have 4 marbles;
• Janae and Jerome each have 5 marbles.