Question

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

Answer 1

It's D.

Explanation:

Edge 2020;)

Answer 2

D) q + d = 330

0.25q + 0.1d = 6

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