Sandy Has $3.25 In Change. She Has Five More Dimes Than Quarters But Twice As Many Nickels As Dimes. Can You Express The Given Information As An Algebraic Equation And Simplify. [You Are Not Required To Solve The Problem.]?
Answer:
Three equations are required for the three variables. N is the number of nickels, D is the number of dimes, and Q is the number of quarters.
5N + 10D + 25Q = 325
D = Q + 5
N = 2D
The second equation can be solved for Q, so that expressions for N and Q can be substituted into the first equation.
D - 5 = Q
5(2D) + 10D + 25(D-5) = 325 (this is your equation before it is simplified)
45D - 125 = 325 (this is your simplified algebraic equation)
Once you find D, then you find the other two variables by
Q = D-5
N = 2D
_____
Even though you lone asked for the equation (given above), I have to put the solution in to preempt a series of answers by people compelled to provide the solution.
The solution is
45D = 450 (add 125 to both sides)
D = 450/45 (divide both sides by 45)
D = 10 ($1.00)
Q = 5 ($1.25)
N = 20 ($1.00)
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