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Alexandra has some dimes and some quarters. She has no more than 21 coins worth a minimum of $3.75 combined. If Alexandra has 4 dimes, determine the minimum number of quarters that she could have. If there are no possible solutions, submit an empty answer.

Respuesta :

Larrysammz

Answer:

A minimum of 10 dimes and 11 quarters is what Alexandra will have

Step-by-step explanation:

Let

d = number of dimes

q = number of quarters

Since she has 21 coins altogether,

d + q = 21------------------------equation 1    

  •  If these coins are worth $3.75 then

0.10 x d + 0.25 x q = 3.75

  • which is 0.10d +.25q =3.75 --------------------------equation 2

where $.10 is the value of one dime and $.25 is the value of one quarter

make d the subject of formula from equation 1 d = 21 -q----------equation 3

 insert it in equation 2

0.10d +0.25q =3.75

0.10(21-q) + 0.25q = 3.75

0.1(21)-0.1q+0.25q=3.75

2.1 +0.15q = 3.75

0.15q  = 3.75-2.1 = 1.65

q = 1.65/0.15 =165/15 =11

  • since we have the value of q insert in equation 3

d = 21 - q

d = 21-11

d = 10

Alexandra has 10 dimes and 11 quarters.

from my calculation i can see that the a minimum of 10 dimes and 11 quarters is what Alexandra will have