5. There are x dictionaries in a bookstore. After 1/8 of them were purchased, 10 more dictionaries were shipped in bringing the total number of dictionaries to 52. What is the value of x?
after 1/8 were purchased, 7/8 were left. So, now we have
7/8 x + 10 = 52
7/8 x = 42
x = 48
To find the value of x, we can first set up an equation based on the given information. Let's break down the problem into steps:
1. Initially, there are x dictionaries in the bookstore.
2. After 1/8 of the dictionaries were purchased, the remaining number of dictionaries is (1 - 1/8) * x = 7/8 * x.
3. After that, 10 more dictionaries were shipped in, increasing the total number of dictionaries to 52.
4. So, the equation becomes (7/8 * x) + 10 = 52.
To solve for x, we can follow these steps:
Step 1: Subtract 10 from both sides of the equation: (7/8 * x) = 52 - 10 = 42.
Step 2: Multiply both sides of the equation by the reciprocal of 7/8, which is 8/7: x = (42) * (8/7).
Step 3: Simplify: x = 48.
Therefore, the value of x, which represents the initial number of dictionaries, is 48.
Let's solve this step-by-step.
Step 1: Let's assume the initial number of dictionaries in the bookstore as x.
Step 2: After 1/8 of them were purchased, the remaining number of dictionaries in the bookstore is (x - (1/8)x) = (7/8)x.
Step 3: 10 more dictionaries were shipped in, so the total number of dictionaries is (7/8)x + 10.
Step 4: According to the problem, the total number of dictionaries is 52.
So, we have the equation: (7/8)x + 10 = 52.
Step 5: Let's solve the equation for x:
(7/8)x = 52 - 10
(7/8)x = 42
To isolate x, we need to multiply both sides of the equation by (8/7):
x = (42)(8/7)
x = 48
Therefore, the value of x is 48.