Dave has a collection of 47 coins. Some are $10 coins and the rest are $20 coins. If the face value is $710, how many of each denomination does he have?

he had twenty three $10 coins and twenty four $20 coins.

Step-by-step explanation:

Let x represent the number of $10 coins that he has.

Let y represent the number of $20 coins that he has.

Dave has a collection of 47 coins. This means that

x + y = 47

Some are $10 coins and the rest are $20 coins. If the face value is $710, it means that

10x + 20y = 710- - - - - - - - - -1

Substituting x = 47 - y into equation 1, it becomes

10(47 - y) + 20y = 710

470 - 10y + 20y = 710

- 10y + 20y = 710 - 470

10y = 240

y = 240/10

y = 24

x = 47 - y = 47 - 24

x = 23

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,