Hilda has $322 worth of
$11 and $13 stock shares. The number of
$11 shares is seven more than twice the number of $13 shares. How many of each type of share does she have?
To solve this problem, let's define the variables:
Let X be the number of $11 stock shares.
Let Y be the number of $13 stock shares.
We are given the following information:
1) The total value of the stock shares is $322.
2) The number of $11 shares is seven more than twice the number of $13 shares.
Based on the given information, we can write two equations:
Equation 1: The value of the $11 stock shares (11X) plus the value of the $13 stock shares (13Y) equals $322.
11X + 13Y = 322
Equation 2: The number of $11 shares (X) is seven more than twice the number of $13 shares (2Y + 7).
X = 2Y + 7
To find the values of X and Y, we can use one of the methods of solving systems of equations, such as substitution or elimination.
Let's solve using the substitution method:
Step 1: Solve Equation 2 for X in terms of Y.
X = 2Y + 7
Step 2: Substitute the value of X in Equation 1.
11(2Y + 7) + 13Y = 322
22Y + 77 + 13Y = 322
35Y + 77 = 322
Step 3: Subtract 77 from both sides.
35Y = 245
Step 4: Divide both sides by 35.
Y = 7
Step 5: Substitute the value of Y back into Equation 2 to find X.
X = 2(7) + 7
X = 14 + 7
X = 21
Therefore, Hilda has 21 $11 stock shares and 7 $13 stock shares.
Let 11 shares =2(x+7)
Then 13 shares+ x
2(x+7)+x=322 This is right. help.