Answer :
The total number of red counters that are in the box is; 728 red counters
- We are told that the box contains 1079 counters.
Let the number of white counters be x.
Let the number of red counters be y.
Let the number of black counters be z.
Thus;
z:x = 2:7
Thus; 2x/7 = z
Also, we are given;
x:y = 3:8
Thus;
8x/3 = y
- Since total number in the box is 1079,then;
x + y + z = 1079
x + (8x/3) + (2x/7) = 1079
Multiply through by 21 to get;
21x + 56x + 6x = 22659
83x = 22659
x = 22659/83
x = 273
2x/7 = z
Thus; z = 2 × 273/7
z = 78
8x/3 = y
y = 8 × 273/3
y = 728
- Thus,there are;
273 white counters
728 red counters
78 black counters.
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Final answer:
Given the ratios of black to white is 2:7, white to red is 3:8, and the total number of counters 1079, we calculate the relation of red counters to the total, then determine that there are 728 red counters in the box.
Explanation:
To find the number of red counters in the box, we need to find the relation of red counters to the total. Given the ratio of black counters to white counters is 2:7 and white counters to red counters is 3:8, we can find the equivalent ratio of black : white : red by multiply the ratios. After that, we find it is 6:21:56. Now that we know the proportion of red counters in the total, we can calculate the exact number of red counters by multiplying the ratio of red to the total times the total number of counters, which is 1079.
From the ratio 6:21:56, the total parts of counters in the box is 6 + 21 + 56 = 83 parts. Each part represents 1079 / 83 = 13 counters. Therefore, red counters' part, which is 56, represents 56 * 13 = 728 counters.
In conclusion, there are 728 red counters in the box.
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