Question

Help with these math questions ASAP

Answer 1

I'll do the first one.

Convert the statements into equations, we can use 'n' for nickels and 'd' for dimes.

"Jennifer has $1.15 in nickels and dimes."

`\sf 0.05n+0.10d=1.15`

"a total of 16 coins"

`\sf n+d=16`

Solve for one of the variables in the 2nd equation, then plug that into the first equation:


`\sf n+d=16`

Subtract d to both sides:


`\sf n=16-d`

Now input '16 - d' for 'n' in the first equation:


`\sf 0.05n+0.10d=1.15`


`\sf 0.05(16-d)+0.10d=1.15`

Distribute 0.05 into the parenthesis(we do this by multiplying it to every term inside of it):


`\sf 0.8-0.05d+0.10d=1.15`

Combine like terms(-0.05d + 0.10d = 0.05d):


`\sf 0.8+0.05d=1.15`

Subtract 0.8 to both sides:


`\sf 0.05d=0.35`

Divide 0.05 to both sides:


`\sf d=7`

Now we can plug this into any of the two equations to find 'n':


`\sf n+d=16`


`\sf n+7=16`

Subtract 7 to both sides:


`\sf n=9`

So she has 9 nickels and 7 dimes.