A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There are 15 different colored flags to choose from but only 7 flags will be flown. Find the number of different signals consisting of 7, if the first flag must be yellow. If the first flag is yellow then the number of different signals consisting of 7 flags is .

Number of nickels: 2,

Number of dimes: 6

Step-by-step explanation:

Say d ⇒ number of dimes, n ⇒ number of nickels; from this we can formulate two equation knowing the cost per dime ⇒ $ 0.1, and the cost per nickel ⇒ $0.05

d + n = 8,

0.1 * d + 0.05 * n = 0.7 ⇒ Let us solve through substitution

d = 8 - n into 0.1 * d + 0.05 * n = 0.7,

0.1 * ( 8 - n ) + 0.05 * n = 0.7,

0.8 - 0.1 * n + 0.05 * n = 0.7,

0.8 - 0.1n + 0.05n = 0.7,

- 0.05n = - 0.1,

Number of nickels: 2 ⇒ Now let us substitute this value into the first equation as to solve for d, dimes

d = 8 - 2,

Number of dimes: 6