I buy x choc ices and y orange ices and spend $2.30. I buy ten ices altogether . the choc ices cost $0.30 each and the orange ices cost $0.20 each. How many of each do I buy?

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I buy x choc ices and y orange ices and spend $2.30. I buy ten ices altogether . the choc ices cost $0.30 each and the orange ices cost $0.20 each. How many of each do I buy?

I understand how to get to two equations from the problem. All the equations thatI tried are not working out. Please help me out!

1 Answer

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Answer 1 · 2018-03-22T17:08:07

$3$ chocolate ices and $7$ orange ices

Explanation:

So the two equations that you are going to make are as follows. The first is about amount, the second is about cost .

Since you bought 10 total, this is the first equation:
$x + y = 10$

Since chocolate ice costs $"30 cents"$ (or $30/100$ of a dollar) and orange ice costs $"20 cents"$ (or $20/100$ of a dollar) we can make this equation:

$0.30x + 0.20y = 2.30$

I'm actually going to multiply that whole equation by $10$ to move the decimal points one places and make it easier to solve:

$3x + 2y = 23$

Now rearrange the first equation to substitute into the second:
$x + y = 10$
$x = 10 - y$

Now substitute:
$3x + 2y = 23$
$3(10-y) + 2y = 23$
$30 - 3y + 2y = 23$
$30 - y = 23$
$-y = - 7$
$y = 7$

You bought $7$ orange ices.

Now put the value of $y$ into an equation to solve for $x$
$x = 10 - y$
$x = 10 - 7$
$x = 3$

You bought $3$ chocolate ices.

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I buy x choc ices and y orange ices and spend $2.30. I buy ten ices altogether . the choc ices cost $0.30 each and the orange ices cost $0.20 each. How many of each do I buy?

I understand how to get to two equations from the problem. All the equations thatI tried are not working out. Please help me out!

1 Answer

Explanation:

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