Q53. - Algebra 2

Question

In 1950, the average price of a car was about $\backslash (2000$. This may sound inexpensive, but the average income in 1950 was much less than it is now. To compare dollar amounts over time, use the formula $V=\frac{A}{S}C$, where A is the old dollar amount, S is the starting year’s Consumer price index (CPI), C is the converting year’s CPI, and V is the current value of the old dollar amount. Buying a car for $\backslash )2000$ in 1950 was like buying a car for how much money in 2000?

Year	Average CPI
1950	42.1
1960	29.6
1970	38.8
1980	82.4
1990	130.7
2000	174.0

Step-by-Step Solution

Answer

Buying a car for $\$2000$ in 1950 was like buying a car for $\$8266$ in 2000

Step 1 - Substitute given values

Substitute 2000 for A, $42.1$ for S and 174 for C in given equation

$\begin{array}{l}V=\frac{A}{S}C\\ V=\frac{2000}{42.1}\left(174\right)\end{array}$

Step 2 - Order of simplification

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

Step 3 - Simplify V = 2000 42 . 1 174

Follow order of simplification

Multiply 2000 with 174 then divide it by $42.1$

$\begin{array}{c}V=\frac{2000\times 174}{42.1}\\ =\frac{348000}{42.1}\\ \approx 8266\end{array}$

Thus, value of car in the year 2000 is about  $\$8266$