Question

Mac and his brother Ted collect coins. Mac's collection contains 8 more than twice as many as Ted's. If the total number of coins in the two collections is 74, how many coins are in each collection?

If x represents the number of coins in Ted's collection, then which expression represents the number of coins in Mac's collection?

x + 2(8)
2(x + 8)
2x + 8

Answer 1

If Ted's collection is x, then Mac's collection is twice as much, or 2x; 8 more than that is 2x+8. The combination of their coins would be (2x+8)+(x) and it equals 74; so the equation is 2x+8+x=74.

2x+8+x=74
3x=66
x=22

Since x represents Ted's collection, Ted has 22 coins and Mac has 52.

Answer 2

Mac = 52, Ted = 22 and the expression is 2x+8.

Explanation:

Mac's collection contains 8 more than twice as many as Ted's. We have that x represents the number of coins in Ted's collection, 8 more implies adding 8 units to the number of coins in Ted's collection and twice implies multiplication by 2 to the Ted's collection. "8 more than twice" implies that first, we multiplied Ted's collection by two and then add 8. Then

Mac's collection is 8+2x.

Now, the total coins in two collections is 74, then we have that

8+2x+x = 74

8+3x = 74

3x = 74-8

3x = 66

x = 66/3

x = 22.

So, Ted's collection has x=22 coins and Mac's collection has 8+2x = 8+2(22) = 8+44 = 52 coins.