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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA clothing store is donating socks to various charities. The store gave 55 regular packs and 55 value packs to a homeless shelter, which contained a total of 420420 pairs of socks. For foster children, the store donated 55 regular packs and 66 value packs, which equaled 456456 pairs. How many pairs of socks are in each pack?\newlineThere are _\_ pairs of socks in each regular pack and _\_ pairs in each value pack.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA clothing store is donating socks to various charities. The store gave 55 regular packs and 55 value packs to a homeless shelter, which contained a total of 420420 pairs of socks. For foster children, the store donated 55 regular packs and 66 value packs, which equaled 456456 pairs. How many pairs of socks are in each pack?\newlineThere are _\_ pairs of socks in each regular pack and _\_ pairs in each value pack.
  1. Define Variables: Let's define the variables:\newlineLet rr be the number of pairs of socks in a regular pack.\newlineLet vv be the number of pairs of socks in a value pack.\newlineWe can write two equations based on the information given:\newlineFor the homeless shelter: 5r+5v=4205r + 5v = 420\newlineFor the foster children: 5r+6v=4565r + 6v = 456
  2. Write Equations: Now, we will use the elimination method to solve the system of equations. We can eliminate one of the variables by subtracting one equation from the other.\newlineSubtract the first equation from the second equation:\newline(5r+6v)−(5r+5v)=456−420(5r + 6v) - (5r + 5v) = 456 - 420\newlineThis simplifies to:\newlinev=36v = 36
  3. Elimination Method: Now that we have the value of vv, we can substitute it back into one of the original equations to find the value of rr. Let's substitute vv into the first equation: 5r+5(36)=4205r + 5(36) = 420 5r+180=4205r + 180 = 420
  4. Substitute Value: Next, we will solve for rr: \newline5r=420−1805r = 420 - 180\newline5r=2405r = 240\newliner=2405r = \frac{240}{5}\newliner=48r = 48
  5. Solve for r: We have found the values for both rr and vv: \newliner=48r = 48 pairs of socks in each regular pack \newlinev=36v = 36 pairs of socks in each value pack

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