A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 100 nails and each large box has 450 nails. The contractor bought 3 more small boxes than large boxes, which altogether had 2500 nails. Determine the number of small boxes purchased and the number of large boxes purchased.

Question

A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 100 nails and each large box has 450 nails. The contractor bought 3 more small boxes than large boxes, which altogether had 2500 nails. Determine the number of small boxes purchased and the number of large boxes purchased.

Answer 1

Let's assume the number of large boxes purchased is x.

So the number of small boxes purchased is x+3.
The total number of nails in the large boxes is 450*x.
The total number of nails in the small boxes is 100*(x+3).
The total number of nails purchased is 450*x + 100*(x+3) = 2500.
Simplifying, we get 450x + 100x + 300 = 2500.
Combining like terms, we get 550x + 300 = 2500.
Subtracting 300 from both sides, we get 550x = 2200.
Dividing both sides by 550, we get x = 4.
Therefore, the contractor purchased 4 large boxes and 4+3 = <<4+3=7>>7 small boxes. Answer: \boxed{7}.

Answer 2

A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $500 and the daily rate for each partner is $1400. The law firm designated 3 times as many associates as partners to the case and was able to charge the client $5800 per day for these lawyers' services. Determine the number of associates assigned to the case and the number of partners assigned to the case.

Answer 3

Let's assume the number of partners assigned to the case is x.

So the number of associates assigned to the case is 3x.
The total cost of the partners per day is $1400 * x.
The total cost of the associates per day is $500 * 3x.
The total cost per day for all lawyers assigned to the case is $1400 * x + $500 * 3x = $5800.
Combining like terms, we get $1400x + $1500x = $5800.
Simplifying, we get $2900x = $5800.
Dividing both sides by $2900, we get x = 2.
Therefore, the law firm assigned 2 partners and 3*2 = <<3*2=6>>6 associates to the case. Answer: \boxed{6}.

Answer 4

To determine the number of small boxes purchased and the number of large boxes purchased, we can set up a system of equations based on the given information.

Let's represent the number of small boxes as S and the number of large boxes as L.

From the given information, we know that:
1. Each small box has 100 nails, so the total number of nails in small boxes can be expressed as 100S.
2. Each large box has 450 nails, so the total number of nails in large boxes can be expressed as 450L.
3. The contractor bought 3 more small boxes than large boxes, so the relationship between S and L can be expressed as S = L + 3.
4. Altogether, the contractor had 2500 nails, so we can express this as the equation 100S + 450L = 2500.

Now, we can solve the system of equations to find the values of S and L.

Substituting S = L + 3 into the equation 100S + 450L = 2500:
100(L + 3) + 450L = 2500
100L + 300 + 450L = 2500
550L + 300 = 2500
550L = 2200
L = 4

Now that we have the value of L, we can substitute it back into S = L + 3 to find S:
S = 4 + 3
S = 7

Therefore, the contractor purchased 7 small boxes and 4 large boxes.