Question

renata is purchasing a condominium for $125,000. she wants to put down a down - payment of 20%. select all the true statements.
the proportion that represents the down payment is $\frac{20}{100}=\frac{125,000}{x}$
the down payment is $25,000.
the proportion that represents the down payment is $\frac{20}{100}=\frac{x}{125,000}$
the down payment is $50,000.
the down payment is $\frac{1}{5}$ of the cost of the house.

Explanation:

Step1: Set up proportion

Let $x$ be the down - payment. The proportion for percentage is $\frac{20}{100}=\frac{x}{125000}$, so the correct proportion is $\frac{20}{100}=\frac{x}{125000}$, not $\frac{20}{100}=\frac{125000}{x}$.

Step2: Solve for $x$

Cross - multiply: $100x = 20\times125000$. Then $100x=2500000$, and $x=\frac{2500000}{100}=25000$. So the down - payment is $25000$.

Step3: Check fraction

Since $20\%=\frac{20}{100}=\frac{1}{5}$, the down - payment is $\frac{1}{5}$ of the cost of the house.

Answer:

The true statements are:

• The down payment is $25,000$.
• The proportion that represents the down payment is $\frac{20}{100}=\frac{x}{125,000}$.
• The down payment is $\frac{1}{5}$ of the cost of the house.