Question: How many dimes does Mark have?
Q + D < 9
IQ = $0.25
ID = $0.10
Statement 1: The total value of Mark's coin is $1.70.
0.25Q + 0.1D = $1.70
$$D=\frac{1.70-0.25Q}{0.1}\ \ \ \ \ \left(make\ D\ the\ subject\ of\ the\ formula\right)$$
Remember that;
Q + D < 9
So, we have
$$\frac{Q}{1}+\frac{1.70-0.25Q}{0.1}\ <9$$
$$0.1Q+1.70-0.25Q\ <0.9$$
$$-0.15Q\ <0.9-1.70$$
$$-0.15Q\ <-0.8$$
$$\frac{\left(-0.15Q\ \right)}{-0.15}<-\frac{0.8}{-0.15}\ \ \ \ \left(divide\ through\ by\ -0.15\right)$$
Note: When diving with a negative coefficient in inequality, the inequality sign will change (i.e '<' will change to '>')
$$Q>5.3$$
From this expression, the quarters are greater than 5. So, if quarters=6 = 6 * $0.25 = $1.5.
Hence, dimes = 2, giving a total of 8 coins.
However, if you take 7 quarters, then the total value will be above $1.70 (i.e which is $1.75). So, quarters = 6 and dimes = 2.
Therefore, statement 1 is SUFFICIENT.
Statement 2: Mark has three dimes as many quarters as he has dimes.
Q = 3D;
There is no information about the total amount. Hence, statement 2 is NOT SUFFICIENT.
Conclusively, since only statement 1 is SUFFICIENT, then the correct answer is Option A.
Thanks
