Wendy has 35 coins in pennies and nickels. She has 1.03$. Write a system of linear equations that could be used to determine the number of nickels she has and the number of pennies she has. What do you know already from the question? Solve the equation.

Answer 1

Let's assume that Wendy has x number of pennies and y number of nickels.

From the question, we know that Wendy has a total of 35 coins. So we can write the equation:

x + y = 35

We also know that the value of all the coins, in cents, is 103 cents. Since there are 100 pennies in a dollar, the value of x pennies is x cents, and since there are 5 cents in a nickel, the value of y nickels is 5y cents. So we can write the equation:

x + 5y = 103

Now we have a system of linear equations:

x + y = 35
x + 5y = 103

To solve this system of equations, we can use the method of substitution.

From the first equation, we can isolate x:

x = 35 - y

Now we substitute this value of x in the second equation:

(35 - y) + 5y = 103

Simplifying the equation:

35 + 4y = 103

Subtracting 35 from both sides:

4y = 68

Dividing both sides by 4:

y = 17

Now we substitute this value of y back into the first equation to find x:

x + 17 = 35

Subtracting 17 from both sides:

x = 18

So Wendy has 18 pennies and 17 nickels.