Final answer:
An equation in standard form for the situation where you have $0.8 in dimes and quarters is 10x + 25y = 80, where x represents the number of dimes and y represents the number of quarters.
Step-by-step explanation:
To create an equation in standard form that represents the situation where you have $0.8 in your backpack in dimes and quarters, let x represent the number of dimes and y represent the number of quarters. Recall that the value of a dime is $0.10 and the value of a quarter is $0.25.
Each dime is worth $0.10, so the total value of the dimes will be 0.10x dollars. Each quarter is worth $0.25, so the total value of the quarters will be 0.25y dollars. The total amount of money is $0.8, so the equation representing this situation in standard form is:
0.10x + 0.25y = 0.8
However, to get the equation in standard form, we usually want integers as coefficients. To eliminate the decimals, we can multiply every term by 100:
10x + 25y = 80
This equation is now in standard form and represents the combination of dimes and quarters adding up to $0.8.