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Bernardo invested $2,000 in two different types of stocks. The first type cost $32 per share, and the second cost $48 per share. Between the two types, he purchased a total of 47 shares. How many shares of the $48-per-share stock did he purchase?

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Bernardo invested $\$2,000$ in two different types of stocks. The first type cost $\$32$ per share, and the second cost $\$48$ per share. Between the two types, he purchased a total of $47$ shares. How many shares of the $\$48$ -per-share stock did he purchase? $\newline$ ◻

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Add and subtract decimals: word problems

Full solution

Q. Bernardo invested

\$2,000

in two different types of stocks. The first type cost

\$32

per share, and the second cost

\$48

per share. Between the two types, he purchased a total of

47

shares. How many shares of the

\$48

-per-share stock did he purchase?

\newline

◻

Define Variables: Let $x$ be the number of shares of the $\$48$ stock and $y$ be the number of shares of the $\$32$ stock. We have two equations: $x + y = 47$ (total shares) and $48x + 32y = 2000$ (total investment).
Express $y$ in terms of $x$ : To solve for $x$ , we can express $y$ in terms of $x$ from the first equation: $y = 47 - x$ .
Substitute into second equation: Substitute $y = 47 - x$ into the second equation: $48x + 32(47 - x) = 2000$ .
Simplify and solve for x: Now, let's simplify and solve for x: $48x + 1504 - 32x = 2000$ .
Combine like terms: Combine like terms: $16x + 1504 = 2000$ .
Subtract to isolate $x$ : Subtract $1504$ from both sides: $16x = 496$ .
Divide to find x: Divide both sides by $16$ to find $x$ : $x = \frac{496}{16}$ .
Calculate final result: Calculate $x$ : $x = 31$ . So, Bernardo purchased $31$ shares of the $\$48$ stock.

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