Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. A clothing store is donating socks to various charities. The store gave 6 regular packs and 4 value packs to a homeless shelter, which contained a total of 312 pairs of socks. For foster children, the store donated 6 regular packs and 6 value packs, which equaled 354 pairs. How many pairs of socks are in each pack? There are _____ pairs of socks in each regular pack and _____ pairs in each value pack.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  A clothing store is donating socks to various charities. The store gave 6 regular packs and  4 value packs to a homeless shelter, which contained a total of 312 pairs of socks. For foster children, the store donated 6 regular packs and  6 value packs, which equaled 354 pairs. How many pairs of socks are in each pack?  There are _____ pairs of socks in each regular pack and _____ pairs in each value pack.

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Set up equations: Set up the system of equations based on the given information. The store gave 6 regular packs and 4 value packs to a homeless shelter, which contained a total of 312 pairs of socks. This can be represented by the equation: 6r + 4v = 312 For foster children, the store donated 6 regular packs and 6 value packs, which equaled 354 pairs. This can be represented by the equation: 6r + 6v = 354 Where r is the number of pairs in a regular pack and v is the number of pairs in a value pack.Write equations: Write the system of equations. 6r + 4v = 312 6r + 6v = 354Elimination method: Solve the system of equations using the elimination method. First, we can subtract the first equation from the second to eliminate r. (6r + 6v) - (6r + 4v) = 354 - 312 6r + 6v - 6r - 4v = 354 - 312 2v = 42Solve for v: Solve for v, the number of pairs in a value pack. 2v = 42 v = 42 / 2 v = 21Substitute and solve for r: Substitute the value of v back into one of the original equations to solve for r. Using the first equation: 6r + 4v = 312 6r + 4(21) = 312 6r + 84 = 312Solve for r: Solve for r, the number of pairs in a regular pack. 6r + 84 = 312 6r = 312 - 84 6r = 228 r = 228 / 6 r = 38Verify solution: Verify the solution by plugging the values of r and v into the second equation. 6r + 6v = 354 6(38) + 6(21) = 354 228 + 126 = 354 354 = 354 The values satisfy the second equation as well.

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