My son has this Math word problem and I can come up with the answer but, I don't know how to explain to him how I got the answer. The problem is:Lauren has collected 150 nickles and dimes. She has 70 more nickles than dimes. How many nickles and how many dimes does she have?
Let's let D = dimes.
D + 70 = 150
D = 150 - 70
D = 80
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To solve this word problem, let's break it down step by step.
Step 1: Understand the problem
Read the problem carefully to understand what information is given and what needs to be solved.
Here's what we know:
- Lauren has collected 150 nickels and dimes.
- The number of nickels is 70 more than the number of dimes.
Step 2: Assign variables
Assign variables to represent the unknown quantities in the problem.
Let's say:
- x = the number of dimes (since dimes are mentioned second).
- x + 70 = the number of nickels (since it is 70 more than the number of dimes).
Step 3: Create equations
Next, we can create an equation based on the information given in the problem.
- The total number of nickels and dimes is 150, so we can add the number of nickels (x + 70) to the number of dimes (x) and set it equal to 150:
(x + 70) + x = 150
Step 4: Solve the equation
Simplify and solve the equation using basic algebraic techniques.
Combine like terms:
2x + 70 = 150
Subtract 70 from both sides of the equation:
2x = 80
Divide both sides of the equation by 2:
x = 40
Step 5: Interpret the answer
Now that we have found the value of x to be 40, we can determine the number of nickels by substituting this value back into the equation we created earlier.
x + 70 = 40 + 70 = 110
So, Lauren has 110 nickels and 40 dimes.