A system of equations that could be used to determine the number of dimes and the number of quarters are:
An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
A system of equations can be defined an algebraic equation that only has two (2) variables and can be solved simultaneously.
In order to solve this word problem, we would assign variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Note: 1 quarter is equal to 0.25 dollar and 1 dime is equal to 0.1 dollar.
q = 2d ......equation 1.
0.25q + 0.1d = 4.20 .......equation 2.
Multiplying eqn. 2 by 100, we have:
25q + 10d = 420 .......equation 3.
Substituting eqn. 1 into eqn. 3, we have:
25(2d) + 10d = 420
50d + 10d = 420
60d = 420
d = 420/60
d = 7 dime.
For the number of quarters, we have:
q = 2d
q = 2(7)
q = 14 quarter.
Read more on equations here: https://brainly.com/question/1511173
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Complete Question:
Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters as dimes. Write a system of equations that could be used to determine the number of dimes and the number of quarters that Sophie has. Define the variables that you use to write the system.
