Question

Question 8 of 25 Ajar contains 40 dimes and nickels. The total value of the coins is $2.25. If d = the number of dimes and n= the number of nickels, this is the system of equations din = 40 0.0d + 0.05n = 2.25 How many of each type of coin are there? Solve the system to answer the question

A. 35 dimes and five nickels
B 5 dimes and 35 nickels
C 20 dimes and 20 nickels
D 10 dimes and 30 nickels ​

Answer 1

Hello,

Answer A: 35 dimes and 5 nickels

Explanation:

Let say

d the number of dimes

n the number of nickels

There are 25 coins: d+n=25

Total value : 0.1*d+0.05n=2.25

`\left\{\begin {array} {ccc}d+n&=&40\\10*d+5*n&=&225\ multiplied\ by\ 100\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}n&=&40-d\\10*d+5*(40-d)&=&225\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}5*d&=&225-200\\n&=&40-d\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}5*d&=&25\\n&=&40-5\\\end {array}\right.\\\\\\\left\{\begin {array} {ccc}d&=&5\\n&=&35\\\end {array}\right.\\\\Proof:\\5*0.1+35*0.05=0.5+1.75=2.25\\`