21 Mercy is buying some bananas on holiday. She can buy five bananas and have 10 cents left over. Or she can buy three bananas and have 50 cents left over a Write an equation using this information. b Solve your equation to find the cost of one banana. C How much money does Mercy have?

Let's denote the cost of one banana as \( x \) (in cents) and the total amount of money Mercy has as \( M \) (in cents). ### a) Write an equation using this information. From the first scenario: - If Mercy buys 5 bananas, she has 10 cents left over: \[ M = 5x + 10 \] From the second scenario: - If Mercy buys 3 bananas, she has 50 cents left over: \[ M = 3x + 50 \] ### b) Solve your equation to find the cost of one banana. Since both expressions equal \( M \), we can set them equal to each other: \[ 5x + 10 = 3x + 50 \] Now, let's solve for \( x \): 1. Subtract \( 3x \) from both sides: \[ 5x - 3x + 10 = 50 \] \[ 2x + 10 = 50 \] 2. Subtract 10 from both sides: \[ 2x = 40 \] 3. Divide by 2: \[ x = 20 \] So, the cost of one banana is \( 20 \) cents. ### c) How much money does Mercy have? Now that we know \( x = 20 \), we can substitute it back into either equation to find \( M \). Let's use the first equation: \[ M = 5x + 10 \] \[ M = 5(20) + 10 \] \[ M = 100 + 10 \] \[ M = 110 \] Thus, Mercy has \( 110 \) cents, or \( 1.10 \) dollars. ### Summary: - Cost of one banana: \( 20 \) cents - Total money Mercy has: \( 110 \) cents (or \( 1.10 \) dollars)