ana bought 12 pieces of gum consisting of only red gum and white gums. The total cost was 1.29 the red gums each cost .03 more than each white gum and she bought fewer red gums than white gums. How many white gums did she buy?

Question

ana bought 12 pieces of gum consisting of only red gum and white gums. The total cost was 1.29 the red gums each cost .03 more than each white gum and she bought fewer red gums than white gums. How many white gums did she buy?

Answer 1

let the number of reds be r, let the number of whites be w

r + w = 12 and r<w and both r and w must be whole numbers

let the price of a white be x cents, then the price of a red is x+3 cents.
clearly x also must be a whole number.

then r(x+3) + wx = 129
rx + 3r + wx = 129
x(r+w) = 129-3r, but r = 12-w
x(12-w+w) = 129-3r

x = (129-3r)/12

we stated that x had to be a whole number, and the only choices for r are:
0,1,2,3,4,5

the only value which gives a whole number for x is when r = 3
then w = 9, and x = 10
so a white costs 10 cents, and a red costs 13 cents.

but 3(10) + 9(13) is not equal to 129

so your data is inconsistent and there is no solution to your question.

Answer 2

Arhgghhh!!!!

Ignore the last two lines of my previous posts, I subbed in the price for the wrong colours.

Obviously 3(13) + 9(10) = 129

So there were 3 reds and 9 whites.

Answer 3

idk, I don't understand the problem

Answer 4

To solve this problem, let's consider the variables:

Let's say the cost of each white gum is "x" dollars.
Since the cost of red gums is $0.03 more, the cost of each red gum would be "x + $0.03."

We know that Ana bought a total of 12 pieces of gum, consisting of red and white gums.
Let's say Ana bought "r" red gums and "w" white gums.

From the given information, we can form two equations:

1) The total cost of the gums:
The cost of each red gum multiplied by the number of red gums, plus the cost of each white gum multiplied by the number of white gums, equals the total cost.
So, (x + $0.03) * r + x * w = $1.29.

2) The number of red gums:
We also know that Ana bought fewer red gums than white gums. So, r < w.

Now, we can solve these equations to find the number of white gums (w) that Ana bought.

First, let's simplify equation 1 by distributing:
xr + $0.03r + xw = $1.29.

Since Ana bought 12 pieces of gum, the total number of gums is given by equation 3:
r + w = 12.

Now, let's manipulate equation 3 to express r in terms of w:
r = 12 - w.

Substituting this value of r in equation 2, we have:
(12 - w) + w = 12.

Simplifying, we get:
12 - w + w = 12,
12 = 12.

As this equation is always true, it means that any value of w could work. So, the number of white gums that Ana bought can be any number between 0 and 12.