Question

Ted has $6.80 in quarters and dimes.The number of dimes is 3 times the number of quarters. Write a system of equations can be used to find q, the number of quarters, and d, the number of dimes,Ted has?

Answer 1

To determine the number of quarters (q) and dimes (d) Ted has, we set up a system of equations: 25q + 10d = 680 for the total value, and d = 3q for the relationship between the quantities of coins. We can solve this system to find the values for q and d.

Step-by-step explanation:

To solve for the number of quarters and dimes Ted has, we can set up two equations that represent the value of the coins and the relationship between the number of each type of coin. Let q represent the number of quarters and d represent the number of dimes.

The first equation is derived from the total value of the coins, which is $6.80. In cents, this is 680 cents. Quarters are worth 25 cents each and dimes are worth 10 cents each, so the value equation is:

25q + 10d = 680 (1)

The second equation comes from the given relationship that the number of dimes is three times the number of quarters:

d = 3q (2)

These two equations form the system of equations that we will solve simultaneously to find the number of quarters and dimes:

• 25q + 10d = 680
• d = 3q

Answer 2

The system of Equations are
`\left \{ {{0.25q+0.1d=6.80} \atop {d=3q}} \right.`

Step-by-step explanation:

Given:

Let the number of dimes be d.

Also let the number of quarters be q.

Total Money = $6.80

Ted has $6.80 in quarters and dimes.

Hence the equation can be framed as;

`0.25q+0.1d=6.80 \ \ \ \ equation \ 1`

Now also given:

The number of dimes is 3 times the number of quarters.

Hence above statement can be framed as;

`d=3q`

Hence The system of Equations are
`\left \{ {{0.25q+0.1d=6.80} \atop {d=3q}} \right.`