Answer :

let x= bread rolls and y = fruit muffins
X+Y=84
and
X-18=(5/6)Y
system of equations, substitute Y because we want X
X-18=(5/6)(84-X)
X-18=70-(5/6)X
(11/6)X=88
X=48 rolls

Answer:

Henry baked 48 rolls.  

Step-by-step explanation:

We are given the following information in the question:

Total number of rolls and fruit muffins baked = 84

Number of rolls given = 18

After giving away 18 rolls there are [tex]\frac{5}{6}[/tex] as many rolls as muffins.

Let x be the number of rolls and y be the number of fruit muffins.

Then, we can write the following equations:

[tex]x + y =84\\(x-18) = \displaystyle\frac{5}{6}y[/tex]

We have two equations in two variables. Solving the two equations, we have:

[tex]y =84-x\\(x-18) = \displaystyle\frac{5}{6}(84-x)\\\Rightarrow 6x - 108 = 420 - 5x\\\Rightarrow 11x = 528\\\rightarrow x = 48\\y = 84-48 = 36[/tex]

Thus, Henry baked 48 rolls and 36 fruit muffins.

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