A collection of nickels and dimes is worth $9.45. If the number of dimes is doubled, the value is$16.65. Find the number of each coin using SUBSTITUTION.

Accepted Solution

Answer:The number of nickels is 45 and the number of dimes is 72.Step-by-step explanation:Letx ----> number of nickelsy ----> number of dimesRemember that[tex]1\ nickel=\$0.05[/tex][tex]1\ dime=\$0.10[/tex]so[tex]0.05x+0.10y=9.45[/tex] ------> equation A[tex]0.05x+0.10(2y)=16.65[/tex][tex]0.05x+0.20y=16.65[/tex] ------> equation BSolve the system by substitutionwe have[tex]0.05x+0.10y=9.45[/tex] ------> equation A[tex]0.05x+0.20y=16.65[/tex] ------> equation BMultiply both equations by 100 both sides[tex]5x+10y=945[/tex] ---->[tex]5x=945-10y[/tex] --> equation C[tex]5x+20y=1,665[/tex] ----> equation Dsubstitute equation C in equation D[tex](945-10y)+20y=1,665[/tex]solve for y[tex]945+10y=1,665[/tex][tex]10y=1,665-945[/tex][tex]10y=720[/tex][tex]y=72\ dimes[/tex]Find the value of x[tex]5x=945-10y[/tex][tex]5x=945-10(72)[/tex][tex]5x=225[/tex][tex]x=45\ nickels[/tex]Alternative MethodSolve the system by graphingRemember that the solution is the intersection point both graphsusing a graphing toolthe solution is the point (45,72)thereforeThe number of nickels is 45 and the number of dimes is 72.