Ricardo has two types of assignments for his class. The number of mini assignments, $m$ , he has is $1$ fewer than twice the number of long assignments, $l$ , he has. If he has $46$ assignments in total, which of the following systems of equations can be used to correctly solve for $m$ and $l$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $m=2 l-1$ $\newline$ $m+l=46$ $\newline$ (B) $m=2 l-1$ $\newline$ $m=l+46$ $\newline$ (C) $l=2 m-1$ $\newline$ $m+l=46$ $\newline$ (D) $l=2 m-1$ $\newline$ $m=l+46$

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Algebra 1

Solve linear equations with variables on both sides: word problems

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Q. Ricardo has two types of assignments for his class. The number of mini assignments,

m

, he has is

1

fewer than twice the number of long assignments,

l

, he has. If he has

46

assignments in total, which of the following systems of equations can be used to correctly solve for

m

and

l

\newline

Choose

1

answer:

\newline

(A)

m=2 l-1

\newline

m+l=46

\newline

(B)

m=2 l-1

\newline

m=l+46

\newline

(C)

l=2 m-1

\newline

m+l=46

\newline

(D)

l=2 m-1

\newline

m=l+46

Write Equations: Step $1$ : Let's write down what we know. Ricardo has mini assignments ( extit{m}) and long assignments ( extit{l}). The problem says that the number of mini assignments is $1$ fewer than twice the number of long assignments. So we can write the first equation as $m = 2l - 1$ .
Total Assignments: Step $2$ : The total number of assignments is $46$ . This means that if we add the number of mini assignments and the number of long assignments, we should get $46$ . So the second equation is $m + l = 46$ .
Check Options: Step $3$ : Now we need to find which answer choice matches our two equations. Let's check each option.
Option (A) Verification: Step $4$ : Option (A) says $m = 2l - 1$ and $m + l = 46$ . This matches our equations from Step $1$ and Step $2$ .
Other Options Check: Step $5$ : Let's check the other options just to be sure. Option (B) says $m = 2l - 1$ and $m = l + 46$ . This doesn't make sense because it suggests that $m$ is equal to two different things.
Incorrect Options: Step $6$ : Option (C) says $l = 2m - 1$ and $m + l = 46$ . This is not what we have because our first equation is about $m$ in terms of $l$ , not the other way around.
Correct Answer: Step $7$ : Option (D) says $l = 2m - 1$ and $m = l + 46$ . Again, this doesn't match our equations.
Correct Answer: Step $7$ : Option (D) says $l = 2m - 1$ and $m = l + 46$ . Again, this doesn't match our equations. Step $8$ : So, the correct answer is the one that matches our equations from Step $1$ and Step $2$ , which is Option (A).