O God I hate word problems! Is there any mechanical way to memorize word problems?
Can anyone just change this Following word prob to equations pls. I can do the rest!
Sam invested $4500, part at 7%, the rest at 8 1/2%. After one year, the interest earned on 7% investment was $150 less than the interest earned on the 8 1/2%. How much was invested T each rate?
Thanks alot!
$1500 invested in 7% one and
$3000 invested in 8.5% one
Word problems can be daunting, but there are strategies you can use to approach them systematically. Breaking down the problem into smaller parts and converting relevant information into equations can help make the process easier. Let's tackle the word problem you provided, step by step.
Step 1: Understand the problem:
Read the problem carefully to understand what the question is asking and what information is provided. In this case, we are asked to find out how much money was invested at each interest rate.
Step 2: Identify the known quantities:
We need to identify the information given in the problem. In this case, we know that Sam invested a total of $4500, with some amount invested at 7% and the rest at 8 1/2%.
Step 3: Assign variables:
We can assign variables to represent the unknown quantities. Let's use "x" for the amount invested at 7% and "4500 - x" for the amount invested at 8 1/2%. Since the total investment is $4500, the sum of these two amounts will equal $4500.
Step 4: Set up equations:
Now, we can convert the given information into equations. We are told that the interest earned on the 7% investment is $150 less than the interest earned on the 8 1/2% investment. Since interest is calculated using the formula: interest = principal * rate * time, we can set up the following equations:
Interest on 7% investment: 0.07 * x
Interest on 8 1/2% investment: 0.085 * (4500 - x)
We also know that the interest earned on the 7% investment is $150 less than the interest earned on the 8 1/2% investment. Therefore, we can set up the equation:
0.085 * (4500 - x) = 0.07 * x + 150
Step 5: Solve the equation:
Now that we have set up the equation, we can solve it to find the value of x, which represents the amount invested at 7%.
0.085 * (4500 - x) = 0.07 * x + 150
Multiply both sides of the equation by 1000 to eliminate decimals:
85 * (4500 - x) = 70 * x + 150000
Expand and simplify:
382500 - 85x = 70x + 150000
Combine like terms:
382500 - 150000 = 70x + 85x
232500 = 155x
Divide both sides by 155:
1500 = x
Hence, the amount invested at 7% is $1500. To find the amount invested at 8 1/2%, we can substitute this value back into the equation we initially set up:
4500 - x = 4500 - 1500 = $3000
Therefore, $1500 was invested at 7% and $3000 was invested at 8 1/2%.
Remember, the process of setting up equations and solving them is a mechanical way to approach word problems. Understanding the problem and breaking it down into smaller parts will help you in solving word problems efficiently.