Martin has a combination of 33 quarters and dimes worth a total of $6. which system of linear equations can be used to find the number of quarters, q, and the number of dimes, d, martin has? a) q + d = 625q + 10d = 33b) q + d = 60.25q + 0.1d = 33c) q + d = 3325q + 10d = 6d) q + d = 330.25q + 0.1d = 6

D) q + d = 330

0.25q + 0.1d = 6

Step-by-step explanation:

Let q= numbers of quarters

d = number of dimes

q + d = 33 (1)

q = 33 - d

xq + yd = 6 (2)

We will consider the options to know the correct answer

From option A

q +d = 6

25q + 10d = 33

This is wrong

Option B

q + d = 60

0.25q + 0.1d = 33

This is also wrong

Option C

q+d = 33

25q + 10d = 6

Put q = 33 -d in equation 2

25(33 - d) + 10q = 6

825 - 25d + 10d = 6

825 - 15d = 6

-15d = 6-825

-15d = -819

d = -819/-15

d= 54.6

This is also wrong because d exceeds the combination.

Option D

q+d = 33

0.25q + 0.1d = 6

Put q = 33 -d in equation 2

0.25(33 - d) + 0.1d = 6

8.25 - 0.25d + 0.1d = 6

8.25 - 0.15d = 6

-0.15d = 6 - 8.25

-0.15d = -2.25

d = -2.25/ -0.15

d = 15

q = 33 - 15

q = 18

This is correct

To divide a number with a surd, we rationalize the surd.

This is done by multiplying both the numerator and the denominator of the surd with the conjugate of the surd (i.e. the surd with the sign in the middle changed).

Therefore, given