On monday, harry had 75\%75% as many toys as teddy did. on tuesday, after harry acquired 3232 more toys and teddy acquired 15\%15% more than he had on monday, harry had as many toys as teddy did. how many toys did harry have on monday?

60

Step-by-step explanation:

We can first define the variables as hh for the number of Harry's toys on Monday and tt for the number of Teddy's toys on Monday.

We know that on Monday, Harry had 75\%75% as many toys as Teddy, so we can write the following equation:

\qquad h=0.75th=0.75t

Hint #2

When we add 3232 toys to Harry's collection, we get h+32h+32. We can also make an adjustment to Teddy's collection, as he acquired 15\%15% more. We can represent that as 1.15t1.15t, as we should add 15\%15% to 100\%100% to get a percent increase.

Now let's make an equation for Tuesday:

\qquad h+32=1.15th+32=1.15t

Hint #3

We also know that h=0.75th=0.75t from the first equation, so we can substitute that in.

\qquad 0.75t + 32 = 1.15t0.75t+32=1.15t

Let's solve by first subtracting 0.75t0.75t from both sides.

\qquad 32 = 0.4t32=0.4t

We can then divide by 0.40.4 to solve for tt, and when we do that, we find that t=80t=80.

Hint #4

Since t=80t=80, we must substitute it into another equation to find hh (the number of toys Harry had on Monday). Let's pick the first equation.

\qquad h=0.75th=0.75t

\qquad h=0.75(80) = 60h=0.75(80)=60

Hint #5

Harry had 60 toys on Monday.

answer: the common difference is -0.10

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