Sally bought some ordinary pencils and 4 times as many special pencils. Each ordinary pencil cost $0.20 and each special pencil cost $0.35. She spent $14.40. How many of each pencil did she buy?
Please show me how you got your answer. Thank you.
thanks for your help!
To solve this problem, let's assign variables to the unknown quantities in the question.
Let's say Sally bought 'x' ordinary pencils and 'y' special pencils.
Based on the information given, we know that the following equations are true:
1. The cost of ordinary pencils: x * $0.20
2. The cost of special pencils: y * $0.35
3. The total amount spent: $14.40
We can set up an equation using these three pieces of information:
x * $0.20 + y * $0.35 = $14.40
Now, let's solve this equation to find the values of 'x' and 'y'.
Multiply the entire equation by 100 to get rid of the decimal points:
20x + 35y = 1440
Let's try to simplify this equation by dividing it by 5:
4x + 7y = 288
To make this problem easier to solve, we can use a technique called "trial and error" or "guess and check" method.
Let's start with a possible number of special pencils (y) and then find the corresponding number of ordinary pencils (x) that makes the equation true.
Let's try y = 10 special pencils:
4x + 7 * 10 = 288
4x + 70 = 288
4x = 288 - 70
4x = 218
x = 218 / 4
x = 54.5
Since we can't have a fraction of a pencil, this combination doesn't work.
Now, let's try y = 20 special pencils:
4x + 7 * 20 = 288
4x + 140 = 288
4x = 288 - 140
4x = 148
x = 148 / 4
x = 37
So, if Sally bought 37 ordinary pencils and 20 special pencils, the total cost would be $14.40, which matches the information given in the question.
Therefore, Sally bought 37 ordinary pencils and 20 special pencils.
Suppose sally bought x no of ordinary prencils.
Therefore, she 4x no of special pencils.
Expenditure on ordinary pencil = $0.20*x
Expenditure on special pencils = $0.35*4x
o.20*x+ 0.35*4x = 14.40
x= 26
so she bought 26 ordinary pencil and 4*26=104 special pencil.