Answer:
65
Step-by-step explanation:
I'm not completely sure if this is correct but this is what I got:
cherry candies: c ; grape candies: g
the ratio of the cherry candies to the grape candies is 3:5 so c/g=3/5 so c=3/5g
when you eat 1 cherry candy and half of the grape candies the ratio becomes (c-1)/(g/2)=7/6
I used substitution so now it becomes (3/5g-1)/(g/2)=7/6 if you solve this g will equal to 60. This number means that there was 60 grape candies originally. With this, you can solve for the number of cherry candies that you originally had (which is 36 because the ratio is 3:5)
so now you halve the number of grape candies which is 30 and take one off from the cherry candies which is now 35 (cherry:grape = 7:6 = 35:30)
there are now 65 candies altogether
A ratio shows us the number of times a number contains another number. The total number of candies that are left in the bag is 65.
A ratio shows us the number of times a number contains another number.
The ratio of cherry candies to grape candies in a bag is 3:5. Therefore, we can write the ratio of the cherry to grapes as,
Cherry / grapes = 3/5
Multiply both the numerator and the denominator of the ratio with x,
Cherry / grapes = 3x/5x
Therefore, the number of Cherry and grapes in the initial was 3x and 5x, respectively.
Further, it is given that your friend eats half of the grape flavored candies and only one cherry flavored candy, the ratio of cherry to grape candies is 7:6. Therefore, we can write the ratio as,
[tex]\dfrac{3x - 1}{\frac{5x}{2}} = \dfrac{7}{6}[/tex]
Now, to get the real numbers we can write,
[tex]\dfrac{3x - 1}{\frac{5x}{2}} = \dfrac{7}{6} \times \dfrac{y}{y}\\\\\dfrac{3x - 1}{\frac{5x}{2}} = \dfrac{7y}{6y}[/tex]
Thus, we got two equations,
3x - 1 = 7y
5x/2 = 6y
Solving the second equation for x,
5x/2 = 6y
5x = 12y
x = 12y/5
Substitute the value of x in the first equation,
3x - 1 = 7y
3(12y/5) - 1 = 7y
y = 5
Furthermore, the total number of candies can be written as,
6y + 7y
= 6(5) + 7(5)
= 30 + 35
= 65
Hence, the total number of candies that are left in the bag is 65.
Learn more about Ratios:
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