Diego works at a toy store. His boss tells him to order 420 stuffed bears and toy cars. He must order 4 stuffed bears for every 3 toy cars.

a) If he must order 9 large stuffed bears for every 7 small stuffed bears, how many of each stuffed bear should he order?

b) If Diego must order 7 toy racecars for every 3 toy trucks, how many of each toy car should he order?

To answer these questions, we can use a method called proportional reasoning. Proportional reasoning is a way to compare quantities and find the relationship between them.

a) Let's first determine the ratio between the number of stuffed bears and toy cars Diego needs to order. The ratio is given as 4:3, which means for every 4 stuffed bears, he needs to order 3 toy cars.

To find the number of stuffed bears and toy cars Diego should order, we can set up a proportion:

4 stuffed bears / 3 toy cars = x stuffed bears / 420 toys

Cross-multiplying, we get:

4 * 420 = 3x
1680 = 3x

Dividing both sides by 3, we find:

x = 1680 / 3 = 560

Therefore, Diego should order 560 stuffed bears and 420 toy cars.

b) Similarly, to find the number of toy racecars and toy trucks Diego should order, we need to set up a proportion. Given that the ratio is 7:3 (toy racecars:toy trucks) and we need to order 420 in total.

7 toy racecars / 3 toy trucks = x toy racecars / 420 toys

Cross-multiplying, we get:

7 * 420 = 3x
2940 = 3x

Dividing both sides by 3, we find:

x = 2940 / 3 = 980

Therefore, Diego should order 980 toy racecars and 420 toy trucks.

b+c = 420 so c = 420 - b

c = (3/4) b
so
3 b/4 = 420 - b
3 b = 1680 - 4 b
7 b = 1680
b = 240 bears total

b = sb + bb but bb = (9/7)sb
so
240 = sb +(9/7) sb = (16/7)sb
sb = 105 small bears
bb = 240 - 105 = 136 big bears
I will leave the last part for you

Need help on b

Yes