A bag contaions 78 boxes of staple pins of two sizes, large and small. Each large box weighs 10g and each small box weighs 7g. If the total weight of the boxes in the bag is 672g. How many of each type are in the bag?
L + S = 78 ... multiplying by 7 ... 7 L + 7 S = 546
10 L + 7 S = 672
subtracting equations (to eliminate S) ... 3 L = 672 - 546
solve for L , then substitute back to find S
Ah, the old staple pin mystery! Let's solve this with a sprinkle of humor. Let's say the number of large boxes is L, and the number of small boxes is S. We have two equations to play with:
Equation #1: L + S = 78 (because we have a total of 78 boxes in the bag)
Equation #2: 10L + 7S = 672 (because the total weight of the boxes is 672g)
Now, let's solve this circus of equations! We'll use substitution. We rearrange Equation #1 to get S = 78 - L. Then, we substitute this value into Equation #2:
10L + 7(78 - L) = 672
After we do some math circus tricks, we end up with:
10L + 546 - 7L = 672
Combine like terms and rearrange:
3L = 126
Divide both sides by 3:
L = 42
Now, substitute this value back into Equation #1 to find S:
42 + S = 78
S = 36
So, juggling with these numbers, we have 42 large boxes and 36 small boxes in the bag. Ta-da!
Let's assume the number of large boxes of staple pins in the bag is L, and the number of small boxes is S.
According to the given information, each large box weighs 10g and each small box weighs 7g. The total weight of all the boxes in the bag is 672g.
So, we can set up the following equation based on the weights:
10L + 7S = 672 ........(1)
We also know that the bag contains a total of 78 boxes:
L + S = 78 ........(2)
We can solve this system of equations (1) and (2) to find the values of L and S.
Let's solve equation (2) for L:
L = 78 - S
Substituting this value of L in equation (1), we get:
10(78 - S) + 7S = 672
Simplifying the equation:
780 - 10S + 7S = 672
-3S = 672 - 780
-3S = -108
Dividing both sides by -3:
S = 36
Now, substitute the value of S back into equation (2) to find L:
L + 36 = 78
L = 78 - 36
L = 42
Therefore, there are 42 large boxes and 36 small boxes in the bag.
To solve this problem, let's assign variables to the unknowns. Let's call the number of large boxes "L" and the number of small boxes "S".
We are given the following information:
- Each large box weighs 10g, and each small box weighs 7g.
- The total weight of the boxes in the bag is 672g.
According to the given information, we can set up two equations based on the weight and number of boxes:
Equation 1: L + S = 78 (since the bag contains a total of 78 boxes)
Equation 2: 10L + 7S = 672 (since the total weight of the boxes is 672g)
To solve these equations, we can use a method called substitution. We can solve Equation 1 for L and express L in terms of S:
L = 78 - S
Now we substitute this value of L in Equation 2:
10(78 - S) + 7S = 672
Simplifying the equation:
780 - 10S + 7S = 672
780 - 3S = 672
-3S = 672 - 780
-3S = -108
S = -108 / -3
S = 36
Now that we have the value of S, we can substitute it back into Equation 1 to find L:
L = 78 - S
L = 78 - 36
L = 42
Therefore, there are 42 large boxes and 36 small boxes in the bag.