A student has a number of $40 and $ 80 savings bonds to use for part otf their college expence.The total value of bonds is $1160.There are 5 more $40 bonds than $80 bonds.How many of each type of bonds she have?
40 x + 80 y = 1160
x - y = 5
Solve for x (the # of $40 bonds) and y(the # of $80 bonds)
To solve this problem, we can use a system of equations. Let's denote the number of $40 bonds as x and the number of $80 bonds as y.
1. The total value of the bonds is $1160. We can express this as an equation:
40x + 80y = 1160
2. There are 5 more $40 bonds than $80 bonds. Mathematically, we can write this as:
x = y + 5
Now we have a system of two equations:
40x + 80y = 1160
x = y + 5
To solve this system, we can use the substitution method or the elimination method. Let's use the substitution method:
Substitute the value of x from the second equation into the first equation:
40(y + 5) + 80y = 1160
40y + 200 + 80y = 1160
120y + 200 = 1160
120y = 1160 - 200
120y = 960
y = 960 / 120
y = 8
Now substitute the value of y back into x = y + 5:
x = 8 + 5
x = 13
Therefore, the student has 13 $40 bonds and 8 $80 bonds.