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A collection of coins contains only 10-cent and 5-cent coins. There are x 5-cent coins in the collection. Find (a) the total value of the 5-cent coins, (b) the total value of the 10-cent coins if there are three times as many 10-cent as 5-cent coins, (c) the total value of the coins if there are seven 5-cent coins for every three 10-cent coins.​

Respuesta :

Let's solve each part of the problem step by step:

(a) **Total value of the 5-cent coins:**
- If there are x 5-cent coins, then the total value of the 5-cent coins is 5*x cents.

(b) **Total value of the 10-cent coins if there are three times as many 10-cent as 5-cent coins:**
- Since there are three times as many 10-cent coins as 5-cent coins, the number of 10-cent coins would be 3x.
- Thus, the total value of the 10-cent coins would be 10 * 3x = 30x cents.

(c) **Total value of the coins if there are seven 5-cent coins for every three 10-cent coins:**
- If there are 7 5-cent coins for every 3 10-cent coins, the ratio of 5-cent coins to 10-cent coins is 7:3.
- Let's denote the number of sets of 7 5-cent coins and 3 10-cent coins as y.
- Therefore, there would be a total of (7y) * 5 cents from the 5-cent coins and (3y) * 10 cents from the 10-cent coins.
- The total value of the coins would be (7y * 5) + (3y * 10) = (35y) + (30y) = 65y cents.

Now, you can calculate the values based on the given information or specific values of x and y.

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