kat has 19 coins, all quarters and dimes, that are worth a total of $4. the system of equations that can be…

kat has 19 coins, all quarters and dimes, that are worth a total of $4. the system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown.\n\nq + d = 19\n0.25q + 0.1d = 4\n\nhow many quarters does she have?\no 4\no 5\no 14\no 15

Answer

Explanation:

Step1: Express d in terms of q

From $q + d=19$, we get $d = 19 - q$.

Step2: Substitute d into the second - equation

Substitute $d = 19 - q$ into $0.25q+0.1d = 4$. $0.25q+0.1(19 - q)=4$.

Step3: Expand and simplify the equation

$0.25q+1.9 - 0.1q=4$. $(0.25q-0.1q)+1.9 = 4$. $0.15q+1.9 = 4$.

Step4: Solve for q

Subtract 1.9 from both sides: $0.15q=4 - 1.9$. $0.15q=2.1$. Divide both sides by 0.15: $q=\frac{2.1}{0.15}=14$.