as of $2009$ , there were about $225$ quarters for every $2$ fifty-cent coins in circulation. if there were about $380$ million quarters in circulation that year, approximately how many total quarters and fifty-cent coins, in millions, were there in circulation

Full solution

Q. as of

2009

, there were about

225

quarters for every

2

fifty-cent coins in circulation. if there were about

380

million quarters in circulation that year, approximately how many total quarters and fifty-cent coins, in millions, were there in circulation

Understand the ratio: Understand the ratio and the given quantity. $\newline$ We are given that there are $225$ quarters for every $2$ fifty-cent coins. We are also given that there are $380$ million quarters in circulation.
Calculate number of coins: Calculate the number of fifty-cent coins based on the given ratio. $\newline$ Since there are $225$ quarters for every $2$ fifty-cent coins, we can set up a proportion to find the number of fifty-cent coins: $\newline$ $\frac{225 \text{ quarters}}{2 \text{ fifty-cent coins}} = \frac{380 \text{ million quarters}}{x \text{ fifty-cent coins}}$
Solve the proportion: Solve the proportion for $x$ , the number of fifty-cent coins. $2 \times 380 \text{ million} = 225 \times x$ $760 \text{ million} = 225x$ $x = \frac{760 \text{ million}}{225}$ $x \approx 3.37777778 \text{ million}$
Round number of coins: Round the number of fifty-cent coins to a reasonable level of precision. Since we are dealing with large numbers and the word ＂about＂ is used, we can round the number of fifty-cent coins to approximately $3.38$ million.
Find total number: Add the number of quarters to the number of fifty-cent coins to find the total. $\newline$ Total in millions = $380$ million quarters + $3.38$ million fifty-cent coins $\newline$ Total in millions $\approx 383.38$ million