At a certain store, 4 knives, 5 spoons, and 6 forks cost $7.90

At a certain store, 4 knives, 5 spoons, and 6 forks cost $7.90. To purchase 2 knives, 2 spoons, and 5 forks would cost $5.80. How much do 2 knives, 3 spoons, and 1 fork cost?
A $2.10
B $3.30
C $4.70
D $5.80

The correct answer and explanation is:

To solve this problem, we can use a system of linear equations. Let’s define the cost of each item:

• Let the cost of one knife be kk,
• Let the cost of one spoon be ss,
• Let the cost of one fork be ff.

We are given two conditions in the problem:

1. The total cost of 4 knives, 5 spoons, and 6 forks is $7.90: 4k+5s+6f=7.904k + 5s + 6f = 7.90
2. The total cost of 2 knives, 2 spoons, and 5 forks is $5.80: 2k+2s+5f=5.802k + 2s + 5f = 5.80

We need to find the cost of 2 knives, 3 spoons, and 1 fork: 2k+3s+f2k + 3s + f

Step 1: Eliminate one variable

Start by simplifying and solving the equations. First, let’s multiply the second equation by 2 to make the number of knives equal in both equations: 2(2k+2s+5f)=2(5.80)2(2k + 2s + 5f) = 2(5.80) 4k+4s+10f=11.604k + 4s + 10f = 11.60

Now subtract the first equation from this new equation to eliminate kk: (4k+4s+10f)−(4k+5s+6f)=11.60−7.90(4k + 4s + 10f) – (4k + 5s + 6f) = 11.60 – 7.90 (4k−4k)+(4s−5s)+(10f−6f)=3.70(4k – 4k) + (4s – 5s) + (10f – 6f) = 3.70 −s+4f=3.70-s + 4f = 3.70

This simplifies to: s=4f−3.70s = 4f – 3.70

Step 2: Substitute into one of the original equations

Substitute s=4f−3.70s = 4f – 3.70 into the first equation 4k+5s+6f=7.904k + 5s + 6f = 7.90: 4k+5(4f−3.70)+6f=7.904k + 5(4f – 3.70) + 6f = 7.90 4k+20f−18.50+6f=7.904k + 20f – 18.50 + 6f = 7.90 4k+26f−18.50=7.904k + 26f – 18.50 = 7.90 4k+26f=26.404k + 26f = 26.40

Step 3: Solve for kk

Now divide both sides by 4: k+6.5f=6.60k + 6.5f = 6.60 k=6.60−6.5fk = 6.60 – 6.5f

Step 4: Solve for the cost of 2 knives, 3 spoons, and 1 fork

Now substitute k=6.60−6.5fk = 6.60 – 6.5f and s=4f−3.70s = 4f – 3.70 into the expression for the cost of 2 knives, 3 spoons, and 1 fork: 2k+3s+f=2(6.60−6.5f)+3(4f−3.70)+f2k + 3s + f = 2(6.60 – 6.5f) + 3(4f – 3.70) + f =13.20−13f+12f−11.10+f= 13.20 – 13f + 12f – 11.10 + f =13.20−11.10=2.10= 13.20 – 11.10 = 2.10

Thus, the cost of 2 knives, 3 spoons, and 1 fork is $2.10.

The correct answer is A.