7. A vending machine only accepts dimes and quarters. There are 85 coinsin the machine with a total value of $16.75. How many of each coin are inthe machine?

There are 55 quarters and 30 dimes in the machine.Step-by-step explanation:Total coins = 85Total amount = $16.75 = 16.75*100 = 1675 cents1 quarter = 25 cents1 dime = 10 centsAccording to given statement; x+y=85    Eqn 125x+10y=1675   Eqn 2Multiplying Eqn 1 by 10[tex]10(x+y=85)\\10x+10y=850\ \ \ Eqn\ 3[/tex]Subtracting Eqn 3 from Eqn 2[tex](25x+10y)-(10x+10y)=1675-850\\25x+10y-10x-10y=825\\15x=825[/tex]Dividing both sides by 15[tex]\frac{15x}{15}=\frac{825}{15}\\x=55[/tex]Putting in Eqn 1;[tex]55+y=85\\y=85-55\\y=30[/tex]There are 55 quarters and 30 dimes in the machine.Keywords: linear equation, subtractionLearn more about linear equations at:brainly.com/question/12497249brainly.com/question/12613605#LearnwithBrainly