Keisha bought cups of coffee and bagels for the people in her office. Each bagel cost $2 and each cup of coffee cost $1.50. Keisha spent a total of $40 to buy 23 items. Let x represent the number of bagels and y represent the number of cups of coffee.

Respuesta :

Answer:

The number of bagels is 11 and the cups of coffee is 12.

Step-by-step explanation:

Given:

Keisha bought cups of coffee and bagels for the people in her office. Each bagel cost $2 and each cup of coffee cost $1.50.

Keisha spent a total of $40 to buy 23 items.

Now, to find the number of cups of bagels and coffee.

As given in question:

Let [tex]x[/tex] represent the number of bagels.

And [tex]y[/tex] represent the number of cups of coffee.

So, the total number of items:

[tex]x+y=23[/tex]

[tex]x=23-y[/tex]    ......(1)

Now, the total money spent on items:

[tex]2x+1.50y=40[/tex]

Substituting the value of [tex]x[/tex] from equation (1):

[tex]2(23-y)+1.50y=40[/tex]

[tex]46-2y+1.50y=40[/tex]

[tex]46-0.50y=40[/tex]

Subtracting both sides by 46 we get:

[tex]-0.50y=-6[/tex]

Dividing both sides by -0.50 we get:

[tex]y=12.[/tex]

The number of cups of coffee = 12.

Now, to get the number of bagel we substitute the value of [tex]y[/tex] in equation (1):

[tex]x=23-y[/tex]

[tex]x=23-12[/tex]

[tex]x=11.[/tex]

The number of bagels = 11.

Therefore, the number of bagels is 11 and the cups of coffee is 12.

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