Henry purchased x apples and Jack purchased 10 apples fewer than one-third of the number of apples Henry purchased. Are these amounts equal?
A-the number of apples Jack purchased
B-x-30 divided by 3
(x/3)-10 = Jack = (x-30)/3
yes, the right and the left are equal, but you can not solve for x without knowing more.
for example if you know jack bought 20 apples
then
20 = (x-30)/3
60 = x-30
x = 90 for Henry
check
90/3 - 10 = 20 for Jack
To answer this question, we need to compare the number of apples purchased by Henry and Jack.
Let's break it down step by step:
1. Henry purchased x apples.
2. Jack purchased 10 apples fewer than one-third of the number of apples Henry purchased.
Let's calculate the number of apples Jack purchased:
Step 1: Calculate one-third of the number of apples Henry purchased:
One-third of x is x/3.
Step 2: Subtract 10 from x/3:
The number of apples Jack purchased is x/3 - 10.
Now, we need to compare this to the expression B = (x - 30) / 3.
So, the comparison we need to make is:
Is x/3 - 10 equal to (x - 30) / 3?
To determine if these amounts are equal, we can set up an equation:
x/3 - 10 = (x - 30) / 3
To solve this equation and find the value of x, we can follow these steps:
1. Multiply the entire equation by 3 to get rid of the denominators:
3 * (x/3 - 10) = 3 * ((x - 30) / 3)
2. Simplify the equation:
x - 30 = x - 30
From this equation, we can see that the left side is equal to the right side. Therefore, the amount of apples Jack purchased (x/3 - 10) is indeed equal to (x - 30) / 3.
So, the answer is YES, these amounts are equal.