Algebra 1Algebra 1

Coin Word ProblemsCoin Word Problems

1)1) Stan’s pocket is filled with nickels Stan’s pocket is filled with nickels and dimes. He has 6 more dimes and dimes. He has 6 more dimes than nickels. All together Stan has than nickels. All together Stan has $1.20 in coins. How many nickels $1.20 in coins. How many nickels and dimes does he have?and dimes does he have?

-Let’s start with the sentence “He has 6 -Let’s start with the sentence “He has 6 more dimes than nickels.”more dimes than nickels.”

-Ask yourself “Which coin does he have -Ask yourself “Which coin does he have more of?”more of?”

-The answer is dimes.-The answer is dimes.

d = n + 6 Quantity Equationd = n + 6 Quantity Equation

All together Stan has $1.20 in All together Stan has $1.20 in coins.coins.

• Each coin has a different value.Each coin has a different value.

• Each nickel is worth 5 cents. Thus 5n Each nickel is worth 5 cents. Thus 5n is the amount all his nickels are worth.is the amount all his nickels are worth.

• Each dime is worth 10 cents. Thus 10d Each dime is worth 10 cents. Thus 10d is the amount all his dimes are worth.is the amount all his dimes are worth.

• $1.20 is worth 120 cents…$1.20 is worth 120 cents…

• 5n + 10d = 120 The value 5n + 10d = 120 The value equation. equation.

Substitute and solveSubstitute and solve

• 10d + 5n = 120 and d = (n + 6)10d + 5n = 120 and d = (n + 6)

• 10(n + 6) + 5n = 12010(n + 6) + 5n = 120

• 10n + 60 + 5n = 12010n + 60 + 5n = 120

• 15n + 60 = 12015n + 60 = 120

• 15n = 6015n = 60

• n = 4 n = 4

Complete the ProblemComplete the Problem

• He has 4 nickels.He has 4 nickels.

• d = n + 6d = n + 6

• d = 4 + 6d = 4 + 6

• d = 10d = 10

• Stan has 4 nickels and 6 dimes. Stan has 4 nickels and 6 dimes.

CheckCheck

• 10 dimes is worth 10(.10) = $1.0010 dimes is worth 10(.10) = $1.00

• 4 nickels is worth 4(.05) = $0.204 nickels is worth 4(.05) = $0.20

Total = $1.20Total = $1.20

4) She gave the sitter 6 more 4) She gave the sitter 6 more nickels than dimes.nickels than dimes.

• She has more…She has more…

• Nickels.Nickels.

• n = d + 6 Quantity Equation.n = d + 6 Quantity Equation.

• She has 3 times as many quarters as She has 3 times as many quarters as dimes.dimes.

• She has more…She has more…

• Quarters.Quarters.

• q =3d Quantity Equation.q =3d Quantity Equation.

All together Mrs. Ryan paid the All together Mrs. Ryan paid the babysitter $7.50.babysitter $7.50.

• Total nickel value in cents…Total nickel value in cents…

• 5n5n

• Total dime value in cents…Total dime value in cents…

• 10d10d

• Total quarter value in cents…Total quarter value in cents…

• 25q25q

• 5n + 10d + 25q = 7505n + 10d + 25q = 750

Substitute and SolveSubstitute and Solve

• n = d + 6 q = 3dn = d + 6 q = 3d

• 5n + 10d + 25q = 7505n + 10d + 25q = 750

• 5(d + 6) + 10d + 25(3d) = 7505(d + 6) + 10d + 25(3d) = 750

• 5d + 30 + 10d + 75d = 7505d + 30 + 10d + 75d = 750

• 90d + 30 = 75090d + 30 = 750

• 90d = 72090d = 720

• d = 8d = 8

• She paid 8 dimes.She paid 8 dimes.

Solve for Nickels and Solve for Nickels and QuartersQuarters

• d = 8d = 8

• n = d + 6n = d + 6

• n = 8 + 6n = 8 + 6

• n = 14n = 14

• q = 3dq = 3d

• q = 3(8)q = 3(8)

• q =24q =24

CheckCheck

• 8 dimes is worth 8($0.10) = 8 dimes is worth 8($0.10) = $0.80$0.80

• 14 nickels is worth 14($0.05) = 14 nickels is worth 14($0.05) = $0.70$0.70

• 24 quarters is worth 24($0.25) = 24 quarters is worth 24($0.25) = $6.00$6.00 Total = $7.50Total = $7.50