A pencil costs $3.50 and a pen costs $6.70. Jessica bought m pens. She also bought 4 fewer pencils than pens. Write an algebraic expression for the total amount she spent and solve the expression.
Sure! Let's break down the problem step by step:
Let's say Jessica bought m pens. Since she bought 4 fewer pencils than pens, the number of pencils she bought will be (m - 4).
The cost of each pen is $6.70, so the total cost of the pens will be 6.70m.
The cost of each pencil is $3.50, so the total cost of the pencils will be 3.50(m - 4).
To find the total amount Jessica spent, we need to add the cost of the pens and the cost of the pencils together:
Total Amount Spent = Cost of Pens + Cost of Pencils
= 6.70m + 3.50(m - 4)
Now, let's solve the expression:
Total Amount Spent = 6.70m + 3.50(m - 4)
Expanding the expression:
Total Amount Spent = 6.70m + 3.50m - 14
Combining like terms:
Total Amount Spent = 10.20m - 14
And that's the algebraic expression for the total amount Jessica spent.
Let's start by defining some variables:
Let p be the price of a pencil.
Let q be the price of a pen.
Let x be the number of pens Jessica bought.
Since she bought 4 fewer pencils than pens, the number of pencils she bought would be (x - 4).
So, the total amount spent on pens would be x * q.
The total amount spent on pencils would be (x - 4) * p.
Therefore, the total amount Jessica spent can be expressed as:
Total amount = (x * q) + ((x - 4) * p)
Given that p = $3.50 and q = $6.70, let's solve the expression for a specific value of x.
Total amount = (x * 6.70) + ((x - 4) * 3.50)
To find the value of x, we need more information/error(s) on the specific amount Jessica spent.
To write an algebraic expression for the total amount Jessica spent, we need to find the cost of the pens and pencils separately.
Let's start with the cost of the pens. We know that each pen costs $6.70, and Jessica bought m pens. Therefore, the cost of the pens would be 6.70m.
Now let's move on to the pencils. We know that each pencil costs $3.50, and Jessica bought 4 fewer pencils than pens. Since she bought m pens, she would have purchased m - 4 pencils. Therefore, the cost of the pencils would be 3.50(m - 4).
To find the total amount Jessica spent, we need to add the cost of the pens and pencils. The algebraic expression for the total amount spent (T) would be:
T = 6.70m + 3.50(m - 4)
Now let's solve this expression:
T = 6.70m + 3.50m - 14
Combining like terms, we have:
T = 10.20m - 14
This is the algebraic expression for the total amount Jessica spent.