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?

Question

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?

Bytelearn · Accepted Answer

Denote shares and equation: Let's denote the number of shares of the $32 stock as x and the number of shares of the $48 stock as y. We know that Bernardo purchased a total of 47 shares, so we can write the first equation as: x + y = 47Total investment equation: We also know that the total amount invested is $2,000. Since the first type of stock costs $32 per share and the second type costs $48 per share, we can write the second equation based on the total investment as: 32x + 48y = 2000Solving system of equations: Now we have a system of two equations with two variables: 1) x + y = 47 2) 32x + 48y = 2000 We can solve this system using substitution or elimination. Let's use the substitution method. From the first equation, we can express x in terms of y: x = 47 - ySubstitute x into equation: Substitute x = 47 - y into the second equation: 32(47 - y) + 48y = 2000 Now, distribute the 32 into the parentheses: 32*47 - 32y + 48y = 2000Simplify and combine terms: Simplify and combine like terms: 1504 - 32y + 48y = 2000 16y = 2000 - 1504 16y = 496Solve for y: Divide both sides by 16 to solve for y: y = 496 / 16 y = 31Check total shares: Now that we have the value for y, which represents the number of shares of the $48 stock, we can check if the total number of shares adds up to 47: x + y = 47 x + 31 = 47 x = 47 - 31 x = 16Check total investment: We found that x = 16 and y = 31. Let's check if the total investment is correct with these numbers: 32x + 48y = 32*16 + 48*31 = 512 + 1488 = 2000

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 \$ 2,000 $2,000 in two different types of stocks. The first type cost $32 \$ 32 $32 per share, and the second cost $48 \$ 48 $48 per share. Between the two types, he purchased a total of 474747 shares. How many shares of the $48 \$ 48 $48-per-share stock did he purchase?

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?