Algebra Honors (Periods 5 & 6)

Solving Problems with Two Variables 9-3

Although the textbook uses charts and tables for these word problems, I think they work easily without the charts...

John has 15 coins -- all dimes and quarters , worth $2.55 How many dimes and quarters does he have?
let d = the number of dimes and let q = the number of quarters
we know d + q = 15 and we know 10d + 25q = 255
using a system of equations and the substitution method
since d + q = 15 we know d = 15- q
10d + 25q - 255
10(15-q) + 25 q = 255
150 -10q + 25q = 255
150 + 15q = 255
15q = 105
q = 7
He has 7 quarters and 8 dimes


Ann and Betty together have $ 60. Ann has $9 more than twice Betty's amount. How much money does each have?
Let a = the amount Ann has and let b = the amount Betty has.
we know
a + b = 60
and we know
a= 2b + 9
so using a + b = 60
(2b+9) + b = 60
3b = 51
b = 17
Betty has $17 and Ann has (60-17) = $43

Joan Wu invested $8000 in stocks and bonds. the stocks pay 4% interest and the onds pay 7% interest . The annual interest from the stocks and bonds is $500.
How much is invested in bonds?
let s = the amount invested in stocks
let b = amount invested in bonds
s + b = 8000
0.04s + 0.07b = 500
clear the decimals
4s + 7b = 50000
but we know s + b = 8000 or s = 8000 -b
4(8000 -b) + 7b = 50000
32000 - 4b + 7b = 50000
3b = 18000
b = 6000
She invested $6000 in bonds.