A woman has 31 coins in her pocket, all of which are dimes and quarters. If the total value of the coins is $ 5.65, how many dimes and how many quarters does she have?

14 dimes and 17 quarters

Step-by-step explanation:

d and q are the number of dimes and quarters, respectively.

"31 coins, all of which are dimes and quarters."

d+q = 31

d = 31-q

"the value of the coins is $5.65"

0.10d + 0.25q = 5.65

substitution

0.10(31-q) + 0.25q = 5.65

3.10-0.10q + 0.25q = 5.65

0.15q = 2.55

q = 17

d = 31-q = 14

14 dimes and 17 quarters

for this case we have the following expression:

to solve, we rewrite the expression as:

we apply double c and we have:

thus, the quotient is 48.

so, patel found a wrong ratio and the multiplication was incorrect.

option d

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!