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He has 22 dimes and 17 nickels \[22\times.10+17\times.05\] \[2.20+0.85\] \[3.05\]
Thank you but can you tell me what formula you used to figure it out...cause that is part of my homework to show the Algebraic equation.
I tried the whole divide 3.05 in half and subtract .50 from one side and add that to the other side but the problem is I don't know how to make an equation out of all that...or even if it would work...this Algebra stuff is soooo difficult.
Getting equations out the description takes practice. You do it enough times, eventually it will "click" Ray has a handful of dimes and nickels valuing $3.05 You have to think, " so many dimes plus so many nickels add up to $3.05" Now the math part: you don't know how many dimes or nickels, but you can give the number a name (people use x and y, or in this case, d and n (easier to remember)) So the first clue is "how many ...." should make you think "unknown number" ... give it a name. so you have d dimes and n nickels the worth of the coins is 3.05, so you need common sense here... if you had 1 dime, how much money do you have. Hopefully you know 1 dime = $0.10 and 2 dimes = $.20 or, in general, if you have d dimes, you have 0.10 * d ... you can think about that, and check that it makes sense: if you have 0 dimes, mean d=0, the expression 0.10*0= 0 says you have 0 dollars. Or if you have 2 dimes (d=2), the expression says you have 0.10*2= 0.20 , which is twenty cents. It should make sense. Use the same idea of nickels. n nickels will be worth 0.05 * n together you have 0.10 d + 0.05 n = 3.05
He has 5 more dimes than he does nickels 5 more dimes than nickels means you have more dimes than nickels. if you had equal number of dimes and nickels, you could say "number of dimes equals number of nickels" or in "math" you could say d = n but here we have 5 more dimes than nickels. If we subtracted the "5 extra" dimes, then the number of dimes would equal the number of nickels: d - 5 = n you could also write that as d= n+5 (if we added 5 to the number of nickels, we would get the number of dimes).
How many of each coin does he have? you have two equations and two unknowns (d and n) 0.10 d + 0.05 n = 3.05 n= d - 5 now the problem is algebra... one way to solve is use "substitution" , in this case, n= d-5, so we can replace n in the first equation with d-5: 0.10 d + 0.05 (d-5) = 3.05 this is an equation with just one unknown, so we can solve for the unknown. the next step is "distribute" the 0.05, which means multiply every term inside the parens by 0.05, like this: 0.10 d + 0.05 d + 0.05* -5 = 3.05 the 0.05*-5 is -0.25 you can combine "like terms" 0.10 d + 0.05 d = 0.15 d Hopefully you know how to do that step. you now have 0.15 d - 0.25 = 3.05 add +0.25 to both sides 0.15 d -0.25 +0.25 = 3.05 +0.25 simplify (of course -0.25 +0.25 is 0) 0.15 d = 3.30 now divide both sides by 0.15 0.15 d/ 0.15 = 3.30/0.15 0.15 divided by itself is 1 (which is why we do this step) d = 3.30/0.15 = 22 now use one of the equations to find n. Pick the simpler equation (why make things tough?) n= d - 5 but we found d= 22 so we have n= 22-5 n= 17 you should now check that these numbers work in the original problem (always good practice)