Al has 76 nickels and dimes worth$5.55. How many of each coins does Al have?
Let x = # nickels and y = # dimes
x = 76 - y
5x + 10y = 555
Substitute 76-y for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
Agree with this solution.
Worth pointing out that x = 76 - y originates from the formula x + y = 76. In case Jay / anyone else can't seem to get that far when solving similar problems on their own.
5x + 10y = 555 because a nickel is worth 5 cents and dime is worth 10, for a total of 555 cents. When doing these in school I would sometimes assign a variable like n and d so I'd never forget what a variable represents or accidentally get them switched around in my answer.
This also carries over nicely when solving problems like these in computer programming.
Good stuff PsyDAG
To solve this problem, we can use algebraic equations to represent the given information.
Let's say Al has "n" nickels and "d" dimes.
According to the problem, Al has a total of 76 coins. So we can write the equation:
n + d = 76 (Equation 1)
The value of the nickels is 5 cents each, and the value of the dimes is 10 cents each. The total value of all the coins is $5.55, which is equivalent to 555 cents. So we can write another equation representing the value in cents:
5n + 10d = 555 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (n and d). We can solve this system of equations to find the values for n and d.
One way to solve the system is by substitution:
From Equation 1, we can express n in terms of d:
n = 76 - d
Substituting n in Equation 2 with the above expression, we get:
5(76 - d) + 10d = 555
380 - 5d + 10d = 555
5d = 555 - 380
5d = 175
d = 35
Now that we know d = 35, we can substitute this value into Equation 1 to find n:
n + 35 = 76
n = 76 - 35
n = 41
Therefore, Al has 41 nickels and 35 dimes.