Solving Algebraically using a system of equations would go as follows:
Equation 1: 0.10x+0.05y<1
Because a dime (x) is worth ten cents (0.10) and a Nickel is worth five cents (0.05) and their collective price must be less than or equal to a dollar
Equation 2: x+y=15
Because the number of coins (dimes + nickels) must equal 15
Solving the system of equations can be done through the elimination or substitution method, here I would prefer using substitution. The second equation can be re-written as x=15-y then substituted into the first equation, this would yield:
0.10(15-y)+0.05y < 1
1.5 - 0.10y+0.05y < 1 Distributive Property
1.5 - 0.05y < 1
- 0.05y < - 0.5 Remember dividing by a negative swaps the inequality
y > 1
The same could be done for y. Solving the second equation for y would give us y = 15-x...
0.10x + 0.05(15-x)<1 distributive property
0.10x + 0.75 - 0.05x <1
0.05x + 0.75 < 1
0.05x < 0.25
x < 5
Therefore, as long as the number of dimes is less than or equal to 5 and the number of nickels is greater than or equal to 1, the equation will be satisfied.
Examples:
5 Dimes, 10 Nickels = $1
4 Dimes, 11 Nickels = $0.95
3 Dimes , 12 Nickels = $0.90
2 Dimes, 13 Nickels = $0.85
1 Dime, 14 Nickels = $0.80
