Gabriel has some purple and yellow marbles. The total mass of all his marbles is 186 g. He has 10 more yellow marbles than purple marbles. The average mass of the purple marbles is 8 g. The average mass of the yellow marbles is 11 g. How many marbles does Gabriel have altogether?
| |
Purple |
Yellow |
Total |
| Number |
1 u |
1 u + 10 |
2 u + 10 |
| Value |
8 |
11 |
|
| Total value |
8 u |
11 u + 110 |
186 |
Total mass of purple marbles
= 1 u x 8
= 8 u
Total mass of yellow marbles
= 11(1 u + 10)
= 11 u + 110
Total mass of the marbles
= 8 u + 11 u + 110
= 19 u + 110
19 u + 110 = 186
19 u = 186 - 110
19 u = 76
1 u = 76 ÷ 19 = 4
Total number of marbles
= 2 u + 10
= 2 x 4 + 10
= 8 + 10
= 110
Answer(s): 110
