Paper clips costing $0.30 each are to be boxed with paper clips costing $0.25 each. The box of clips will cost $5.70. Of four times the number of $0.30 clips is the same as three times the number rod $0.25 clips, find the number of each type in the box.

the number of clips in the box costing $0.30 each is 9

the number of clips in the box costing $0.25 each is 12

Step-by-step explanation:

Let x represent the number of clips costing $0.30 each in the box.

Let y represent the number of clips costing $0.25 each in the box.

Paper clips costing $0.30 each are to be boxed with paper clips costing $0.25 each. The box of clips will cost $5.70. It means that

0.3x + 0.25y = 5.7- - - - - - - - - 1

If four times the number of $0.30 clips is the same as three times the number of $0.25 clips, it means that

4x = 3y

x = 3y/4

Substituting x = 3y/4 into equation 1, it becomes

0.3 × 3y/4 + 0.25y = 5.7

0.225y + 0.25y = 5.7

0.475y = 5.7

y = 5.7/0.475

y = 12

x = 3y/4 = (3 × 12)/4

x = 9