Question

The ratio of Julia’s peas to Vlada’s peas was 3:2. After Julia gave 15 peas to Vlada, she still had 10 more peas than Vlada. How many peas did Julia have to start with?

Answer 1

So.. hmm let's say. Julia had originally "j" amount of peas,
and Vlada had "v" amount, so

$\bf \textit{Julia(j) had more peas than Vlada(v), by a ratio of 3:2, or }\frac{3}{2} \\ \quad \\ \cfrac{j}{v}=\cfrac{3}{2} \\ \quad \\ \textit{now, Julia gave Vlada 15, so v+15, and Julia, is no longer}\\ \textit{3:2 ratio with Vlada, but only has 10 peas more than Vlada}\\ or\\ v+15=j+10 \\ \quad \\ \quad \\ \begin{cases} \cfrac{j}{v}=\cfrac{3}{2}\implies \boxed{\cfrac{2j}{3}}=v \\ \quad \\ v+15=j+10\\ ----------\\ \boxed{\cfrac{2j}{3}}+15=j+10 \end{cases}$

solve for "j", to see how many Julia originally had

Answer 2

Answer:

120 peas did Julia have to start with

Step-by-step explanation:

As per the statement: The ratio of Julia’s peas to Vlada’s peas was 3:2

Let the number be x;

Then;

Julia have number of peas to start with= 3x and Vlada's have number of peas start with = 2x

Also, it given that  Julia gave 15 peas to Vlada, she still had 10 more peas than Vlada.

⇒ 3x - 15 = 2x + 10 + 15

3x -15 = 2x + 25

Add 15 both sides we get;

3x = 2x + 40

Subtract 2x from both sides we get;

x = 40

Number of peas Julia have = 3x = 3(40) = 120

and

Number of peas Vlada have = 2x = 2(40) = 80

Therefore, Julia have to start with 120 peas