i can't solve these two questions

1. In an office​ building, 52 offices are currently being rented. This represents 40​% of the total units. How many offices are there in the​ building?

2. The sales tax is ​$43 on the purchase of a dining room set for ​$1075. Find the sales tax rate.

#1. 0.40 x = 52

#2. x = 43/1075 * 100%

1. ? i can't figure out.

for # 2. i got 172‬

r * 1075 = 43

r = 43/1075 * 100% = 4 %.

Sure! Let me help you solve these two questions step by step:

1. To find the total number of offices in the building, we can use the concept of percentages. We know that 52 offices represent 40% of the total units.

To find the total number of units in the building, we can set up a proportion:

(52 / x) = (40 / 100)

Cross multiplying gives:
52 * 100 = 40 * x

Simplifying the equation, we get:
5200 = 40x

Now we can solve for x by dividing both sides of the equation by 40:
x = 5200 / 40

Simplifying the equation further, we get:
x = 130

Therefore, there are 130 offices in the building.

2. To find the sales tax rate, we can use the formula:

Sales tax amount = Purchase amount * Sales tax rate

We are given that the sales tax amount is $43 and the purchase amount is $1075. We need to find the sales tax rate.

Rearranging the formula, we get:
Sales tax rate = sales tax amount / purchase amount

Plugging in the values we know, we obtain:
Sales tax rate = 43 / 1075

Now, we can divide these two numbers:
Sales tax rate = 0.04

Multiplying it by 100 to express it as a percentage, we find that the sales tax rate is 4%.

Therefore, the sales tax rate on the purchase of the dining room set is 4%.