A student has a number of $40 dollar and $80 dollar savings bonds to use for part of her expenses for college. The total value of the bonds is $1000. There are 7 more $40 bonds than $80 bonds. How many of each type of bond does she have?
If there are x at $40 and y at $80, then
40x+80y = 1000
x = y+80
Now just solve for x and y
To solve this problem, let's define two variables:
Let's say x represents the number of $80 bonds
Let's say y represents the number of $40 bonds
From the problem description, we can create two equations:
Equation 1: The total value of the bonds is $1000. So, the equation would be:
80x + 40y = 1000
Equation 2: There are 7 more $40 bonds than $80 bonds. So, the equation would be:
y = x + 7
We can solve this system of equations by substituting equation 2 into equation 1.
Substituting y = x + 7 into equation 1:
80x + 40(x + 7) = 1000
Simplifying the equation:
80x + 40x + 280 = 1000
Combining like terms:
120x + 280 = 1000
Subtracting 280 from both sides:
120x = 720
Dividing both sides by 120:
x = 720/120
x = 6
Now that we know x = 6, we can substitute this value back into equation 2 to find the value of y:
y = x + 7
y = 6 + 7
y = 13
Therefore, the student has 6 $80 bonds and 13 $40 bonds.