**Here is a link to practice problems for simultaneous equations.**The coin problems all use elimination instead of substitution. Here are the same coin problems using substitution, with the answers in the comment below.

a) 100 coins, all quarters and pennies, total = $13.72

b) 100 tickets, all children ($6) and adult ($12), total =$912

c) 100 coins, all quarters and nickels, total = $8.20

d) 100 coins, all dimes and pennies, total = $3.79

e) 100 coins, all dimes and nickels, total = $7.85

f) 100 coins, all quarters and dimes, total = $14.65

## 1 comment:

a) 100 coins, all quarters and pennies, total = $13.72

q + p = 100

25q + p = 1372

Use the first equation to get p = 100 - q

The second equation becomes

25q + 100 - q = 1372

24q + 100 = 1372

24q = 1272

q = 1272/24 =

53p = 100 - 53 =

47b) 100 tickets, all children ($6) and adult ($12), total =$912

c + a = 100

6c + 12a = 912

Use the first equation to get c = 100 - a

The second equation becomes

6(100 - a) + 12a = 912

600 - 6a + 12a = 912

600 + 6a = 912

6a = 312

a = 312/6 =

52c = 100 - 52 =

48c) 100 coins, all quarters and nickels, total = $8.20

q + n = 100

25q + 5n = 820

Use the first equation to get n = 100 - q

The second equation becomes

25q + 5(100 - q) = 820

25q + 500 - 5q = 820

20q + 500 = 820

20q = 320

q = 320/20 =

16c = 100 - 16 =

84d) 100 coins, all dimes and pennies, total = $3.79

d + p = 100

10d + p = 379

Use the first equation to get p = 100 - d

The second equation becomes

10d + 100 - d = 379

9d + 100 = 379

9d = 279

d = 279/9 =

31p = 100 - 31 =

69e) 100 coins, all dimes and nickels, total = $7.85

d + n = 100

10d + 5n = 785

Use the first equation to get n = 100 - d

The second equation becomes

10d + 5(100 - d) = 785

10d + 500 - 5d = 785

5d + 500 = 785

5d = 285

d = 285/5 =

55n = 100 - 55 =

45f) 100 coins, all quarters and dimes, total = $14.65

q + d = 100

25q + 10d = 1465

Use the first equation to get d = 100 - q

The second equation becomes

25q + 10(100 - q) = 1465

25q + 1000 - 10q = 1465

15q + 1000 = 1465

15q = 465

q = 465/15 =

31d = 100 - 31 =

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