Word Problems – Number and Value Problems

System of Equations Word Problems

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Students learn to solve number and value word problems using a system of linear equations, as demonstrated in the following problem. Rodolfo has a total of 17 dimes and quarters worth $3.05. How many of each coin does he have? The two variables used in this problem are d, number of dimes, and q, number of quarters. Since Rodolfo has a total 17 dimes and quarters, one equation is d + q = 17. Since the value of his coins is $3.05, the other equation is 10d + 25q = 305. Note that since d represents the number of dimes, 10d represents the value of the dimes. And since q represents the number of quarters, 25q represents the value of the quarters.
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