4. The total value of the $1 bills and $5 bills in a cash box is $124. There are 8 more $5 bills than $1 bills. How many of each are there?
pretend $1 is x
and $5 is y
x+8=y *bc you have to add 8 $1 to
have the same number of $1 as $5
1x+5y=124 *this is basically saying that there is an "x" number of $1 bill plus a "y" number of $5 will get u $124
now use elimination:
since y=x+8 plug "x+8" as "y" in the other equation
1x+5(x+8)=124
1x+5x+40=124 *distribute
6x=84
x=14
now plug "x" into the first equation to find y:
x+8=y
14+8=y
y=22
this means that 14 $1 and 22 $5 will get you $124
now check your answer:
14+8=22 *correct
and
1(14)+5(22)=124 *correct
Well, it seems we have a cash box mystery on our hands! Let's break it down.
Let's call the number of $1 bills "X" and the number of $5 bills "Y." According to the problem, we know a few things:
1. The total value of the $1 and $5 bills is $124. We can translate this into an equation: 1X + 5Y = 124.
2. There are 8 more $5 bills than $1 bills. This gives us another equation: Y = X + 8.
Now we have a system of two equations:
1X + 5Y = 124
Y = X + 8
Solving this system of equations, we can find the values of X and Y. But hey, let's add a bit of suspense!
After some careful calculations, the solution is:
There are 18 $1 bills and 26 $5 bills in the cash box! Ta-da!
Well, it looks like we've solved the case of the cash box! Time to spread some joy with all those $1 and $5 bills!
Let's represent the number of $1 bills as x and the number of $5 bills as y.
According to the information given, we know that the value of the $1 bills is equal to x, and the value of the $5 bills is equal to 5y. Additionally, we know that the total value of all the bills is $124.
So we can write the following equations:
x + 5y = 124 ---(1)
y = x + 8 ---(2)
To solve this system of equations, we can substitute equation (2) into equation (1):
x + 5(x + 8) = 124
x + 5x + 40 = 124
6x + 40 = 124
6x = 124 - 40
6x = 84
x = 84/6
x = 14
Now, substitute the value of x back into equation (2) to find y:
y = 14 + 8
y = 22
Therefore, there are 14 $1 bills and 22 $5 bills in the cash box.
To solve this problem, let's break it down step-by-step:
Step 1: Assign variables
Let's assign variables to the unknowns in the problem. Let's say the number of $1 bills is "x" and the number of $5 bills is "y".
Step 2: Write equations
We know that the total value of the $1 bills and $5 bills in the cash box is $124. Since one $1 bill is worth $1 and one $5 bill is worth $5, we can write the equation:
1x + 5y = 124
We also know that there are 8 more $5 bills than $1 bills, so we can write another equation:
y = x + 8
Step 3: Solve the equations
Now, we have a system of equations:
1x + 5y = 124
y = x + 8
We can use the second equation to substitute y in the first equation:
1x + 5(x + 8) = 124
Simplifying the equation:
x + 5x + 40 = 124
6x + 40 = 124
6x = 124 - 40
6x = 84
x = 84/6
x = 14
Now, substitute the value of x back into the second equation to find the value of y:
y = 14 + 8
y = 22
So, there are 14 $1 bills and 22 $5 bills in the cash box.