Meena went to a bank to withdraw \( \$ 1460 \). She asked the cashier to give her \( \$ 10 \) and \( \$ 100 \) notes only. Meena got 29 notes in all. Find how many notes of \( \$ 10 \) and \( \$ 100 \) she received.

Let's denote the number of $10 notes as \( x \) and the number of $100 notes as \( y \). Since Meena received a total of 29 notes, we can write the equation: \[ x + y = 29 \] The total amount Meena withdrew is $1460, so the total value of the $10 notes and $100 notes is: \[ 10x + 100y = 1460 \] We have a system of two equations: \[ x + y = 29 \] \[ 10x + 100y = 1460 \] We can solve this system of equations to find the values of \( x \) and \( y \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+y=29\\10x+100y=1460\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=29-y\\10x+100y=1460\end{array}\right.\) - step2: Substitute the value of \(x:\) \(10\left(29-y\right)+100y=1460\) - step3: Simplify: \(290+90y=1460\) - step4: Move the constant to the right side: \(90y=1460-290\) - step5: Subtract the numbers: \(90y=1170\) - step6: Divide both sides: \(\frac{90y}{90}=\frac{1170}{90}\) - step7: Divide the numbers: \(y=13\) - step8: Substitute the value of \(y:\) \(x=29-13\) - step9: Simplify: \(x=16\) - step10: Calculate: \(\left\{ \begin{array}{l}x=16\\y=13\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=16\\y=13\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(16,13\right)\) The solution to the system of equations is \( x = 16 \) and \( y = 13 \). Therefore, Meena received 16 notes of $10 and 13 notes of $100.