Emily R. answered • 11/03/22
Patient and Versatile Math Tutor
First, define your variables:
Let m represent how many candy bars Maria sold.
Let t represent how many candy bars Tim sold.
Let's begin by reading the word problem piece by piece.
First, we know that the two of them sold 137 candy bars in total. We can represent this mathematically through the expression:
m + t = 137
Now, the harder part of the problem to interpret: "Maria sold 7 less than twice the number of candy bars that Tim sold."
'Maria sold' indicates that we are trying to describe how many candy bars Maria sold, or (m), as we defined earlier.
'7 less than': language such as 'x less/fewer than' or 'x more/greater than' generally suggest addition or subtraction.
'Twice the number of candy bars': language such as 'twice' or 'three times' generally suggest multiplication.
Finally, 'the number of candy bars that Tim sold'. We defined our variables at the beginning of the problem; we can substitute this for t, which we use to represent the number of candy bars sold by Tim.
Putting all of this together, we know that we are multiplying the number of candy bars Tim sells (t) by two and subtracting by 7. This gives us a number that is 7 less than double the number of candy bars Tim sold.
the number of candy bars Maria sold = ( 2 x the number of candy bars Tim sold ) - 7
m = 2t - 7
Now that we have two equations, we can substitute and solve for each variable. It's easy to substitute m into the first equation because the second equation already defines what m is equal to. Make sure that if you add/subtract or multiply/divide, you do it on both sides of the equation.
m + t = 137
m = 2t - 7
m + t = 137
(2t - 7) + t = 137 substitute m = 2t - 7
3t - 7 = 137
+7 +7
3t = 144
3t/3 = 144/3
t = 48
Now that we know that (t = 48), we can substitute it back into the equation to solve for m. You can substitute it into either equation.
m + t = 137
m + (48) = 137
-48 -48
m = 89
Hope that answered your question!
